Maths-
General
Easy

Question

Find the height of a cuboid whose base area is 180cm2 and volume is 900cm2

  1. 9 cm 
  2. 10 cm
  3. 5 cm
  4. 3 cm

Hint:

 Volume of cuboid is the total space occupied by the cuboid in a three-dimensional space. A cuboid is a three-dimensional structure having six rectangular faces. These six faces of the cuboid exist as a pair of three parallel faces. Therefore, the volume is a measure based on the dimensions of these faces, i.e. length, width and height. It is measured in cubic units.

The correct answer is: 5 cm


    Volume of cuboid = Base area × Height  [Cubic units]
    The base of the cuboid is rectangle in shape. So, the base area of a cuboid is equal to the product of its length and breadth. Hence,
    Volume of a cuboid = length × breadth × height    [cubic units]
    or
    Volume of a cuboid = l × b × h    [cubic units]
    Where,
    • l = length
    • b = breadth
    • h = height
    We have given that,
    Base area of cuboid = length × breadth = 180 cm²
    Volume of cuboid = length × breadth × height = 900 cm³
    • We will get,
    Volume of a cuboid = Base area of cuboid × height of the cuboid
    900 cm³ = 180 cm² × height
    • On dividing both sides by 180 we get,
    height = 900 over 180 = 5 cm
    Thus, the height of the cuboid is 5 cm.
    The correct option is c) 5 cm .

    Related Questions to study

    General
    Maths-

    A cone has a circular base of radius 6m and volume 84π m³. The height of cone is

    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Radius , r = 6 m
    Volume of cone = 84π m³
    We have to find the height of the given cone
    Let height of the cone be h
    We know that
    Volume of a cone = (1 third)πr2h
    84π = (1 third) π (6 x 6) (h)
    Divide both sides of equation by π
    84 = (2 x 6) (h)
    84 = 12h)
    h = 84 over 12
    h = 7 m
    Therefore correct option is a) 7m

    A cone has a circular base of radius 6m and volume 84π m³. The height of cone is

    Maths-General
    Hint:- Volume of a cone = (1 third)πr2h
    Solution :- We have given the dimensions of a cone
    Radius , r = 6 m
    Volume of cone = 84π m³
    We have to find the height of the given cone
    Let height of the cone be h
    We know that
    Volume of a cone = (1 third)πr2h
    84π = (1 third) π (6 x 6) (h)
    Divide both sides of equation by π
    84 = (2 x 6) (h)
    84 = 12h)
    h = 84 over 12
    h = 7 m
    Therefore correct option is a) 7m
    General
    Maths-

    What is the factored form of  50 x squared minus 32 y squared ?

    HINT :- using the formula  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis factorize the given expression
    Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.
    Explanation :-
    Given,50 x squared minus 32 y squared
    Taking out common factor 2 out of equation , we get 2 open parentheses 25 x squared minus 16 y squared close parentheses
    Write 25 x squared text  as  end text left parenthesis 5 x right parenthesis squared text  and  end text 16 y squared text  as  end text left parenthesis 4 y right parenthesis squared text  we get  end text 2 open parentheses left parenthesis 5 x right parenthesis squared minus left parenthesis 4 y right parenthesis squared close parentheses
    Applying  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    We get , 50 x squared minus 32 y squared equals 2 left parenthesis 5 x plus 4 y right parenthesis left parenthesis 5 x minus 4 y right parenthesis
    ∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.

    What is the factored form of  50 x squared minus 32 y squared ?

    Maths-General
    HINT :- using the formula  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis factorize the given expression
    Ans:- 2 (5x + 4)(5x - 4) is the factorized form of the given expression.
    Explanation :-
    Given,50 x squared minus 32 y squared
    Taking out common factor 2 out of equation , we get 2 open parentheses 25 x squared minus 16 y squared close parentheses
    Write 25 x squared text  as  end text left parenthesis 5 x right parenthesis squared text  and  end text 16 y squared text  as  end text left parenthesis 4 y right parenthesis squared text  we get  end text 2 open parentheses left parenthesis 5 x right parenthesis squared minus left parenthesis 4 y right parenthesis squared close parentheses
    Applying  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    We get , 50 x squared minus 32 y squared equals 2 left parenthesis 5 x plus 4 y right parenthesis left parenthesis 5 x minus 4 y right parenthesis
    ∴ 2(5x+4y)(5x-4y) is the factorized form of the given expression.
    General
    Maths-

    Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.

    Hint:- Slant height L = square root of h squared plus r squared end root
    where h is height
    r is radius of base of cone

    Solution:- We have given the dimensions of a right circular cone
    Base diameter = 14 cm
    Radius, r = 14 over 2 = 7 cm
    Height, h = 24 cmsquare root of 625
    Let us find the slant height
    L = square root of h squared plus r squared end root
    L = square root of 24 squared plus 7 squared end root
    square root of 576 plus 49 end root
    square root of 625
    L = 25 cm
    Therefore, the correct option is d) 25 cm.

    Find the slant height of the right circular cone if the base diameter of the right circular cone is 14 cm and the height is 24 cm.

    Maths-General
    Hint:- Slant height L = square root of h squared plus r squared end root
    where h is height
    r is radius of base of cone

    Solution:- We have given the dimensions of a right circular cone
    Base diameter = 14 cm
    Radius, r = 14 over 2 = 7 cm
    Height, h = 24 cmsquare root of 625
    Let us find the slant height
    L = square root of h squared plus r squared end root
    L = square root of 24 squared plus 7 squared end root
    square root of 576 plus 49 end root
    square root of 625
    L = 25 cm
    Therefore, the correct option is d) 25 cm.
    parallel
    General
    Maths-

    Factor the given expression completely.
    64 x squared y squared minus 144 z squared

    HINT :- using the formula a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis factorize the given expression
    Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.
    Explanation :-
    Given, 64 x squared y squared minus 144 z squared
    Taking out common factor 16 out of equation , we get 16 open parentheses 4 x squared y squared minus 9 z squared close parentheses
    Write 4 x squared y squared text  as  end text left parenthesis 2 x y right parenthesis squared text  and  end text 9 z squared text  as  end text left parenthesis 3 z right parenthesis squared text  we get  end text 16 open parentheses left parenthesis 2 x y right parenthesis squared minus left parenthesis 3 z right parenthesis squared close parentheses
    Applying a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    Here a = 2xy ; b = 3z
    We get , 64 x squared y squared minus 144 z squared equals 16 left parenthesis 2 x y plus 3 z right parenthesis left parenthesis 2 x y minus 3 z right parenthesis
    ∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.

    Factor the given expression completely.
    64 x squared y squared minus 144 z squared

    Maths-General
    HINT :- using the formula a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis factorize the given expression
    Ans:- 16 (2xy + 3z) (2xy - 3z) is the factorized form of the given expression.
    Explanation :-
    Given, 64 x squared y squared minus 144 z squared
    Taking out common factor 16 out of equation , we get 16 open parentheses 4 x squared y squared minus 9 z squared close parentheses
    Write 4 x squared y squared text  as  end text left parenthesis 2 x y right parenthesis squared text  and  end text 9 z squared text  as  end text left parenthesis 3 z right parenthesis squared text  we get  end text 16 open parentheses left parenthesis 2 x y right parenthesis squared minus left parenthesis 3 z right parenthesis squared close parentheses
    Applying a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    Here a = 2xy ; b = 3z
    We get , 64 x squared y squared minus 144 z squared equals 16 left parenthesis 2 x y plus 3 z right parenthesis left parenthesis 2 x y minus 3 z right parenthesis
    ∴ 16 ( 2xy + 3z ) ( 2xy - 3z ) is the factorized form of the given expression.

    General
    Maths-

    Dimensions of a rectangular box are 20mx5mx6m,find the difference between T.S.A and L.S.A

    • Step 1:We have given area of one face of the cube.
    Area of face = 81
    • Step 2: For total surface area, find out the product of the square of side length by 6.
    Surface area =  6 (area of face)
                          =  6 (81)
                          =   486
    • Step 4: Therefore, the surface of the given cube is 486.
    • Therefore, the correct answer is option A) 486 .

    Dimensions of a rectangular box are 20mx5mx6m,find the difference between T.S.A and L.S.A

    Maths-General
    • Step 1:We have given area of one face of the cube.
    Area of face = 81
    • Step 2: For total surface area, find out the product of the square of side length by 6.
    Surface area =  6 (area of face)
                          =  6 (81)
                          =   486
    • Step 4: Therefore, the surface of the given cube is 486.
    • Therefore, the correct answer is option A) 486 .
    General
    Maths-

    A funnel is in the shape of a right circular cone with a base radius of 3 cm and a height of 4 cm. Find the slant height of the funnel

    Hint:- Slant height L = square root of n squared plus r squared end root
    where h is height
    r is radius of base of cone
    Solution:- We have given the dimensions of funnel in the shape of cone
    Radius, r = 3 cm
    Height, h = 4 cm
    Let us find the slant height
    L = square root of h squared plus r squared end root
    L = square root of 4 squared plus 3 squared end root
    square root of 16 plus 9 end root
    square root of 25
    L = 5 cm
    Therefore, the correct option is b) 5 cm.

    A funnel is in the shape of a right circular cone with a base radius of 3 cm and a height of 4 cm. Find the slant height of the funnel

    Maths-General
    Hint:- Slant height L = square root of n squared plus r squared end root
    where h is height
    r is radius of base of cone
    Solution:- We have given the dimensions of funnel in the shape of cone
    Radius, r = 3 cm
    Height, h = 4 cm
    Let us find the slant height
    L = square root of h squared plus r squared end root
    L = square root of 4 squared plus 3 squared end root
    square root of 16 plus 9 end root
    square root of 25
    L = 5 cm
    Therefore, the correct option is b) 5 cm.
    parallel
    General
    Maths-

    Factor the polynomial as the product of binomials.
    x squared minus 1 over 9

    Ans :-  open parentheses x minus 1 third close parentheses open parentheses x plus 1 third close parentheses is the required product of binomials.
    Given , x squared minus 1 over 9
    Write text end text 1 over 9 text  as  end text open parentheses 1 third close parentheses squared text  then we get  end text x squared minus open parentheses 1 third close parentheses squared
    As  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    Here a = x and b = 1 third

    x squared minus 1 over 9 equals open parentheses x minus 1 third close parentheses open parentheses x plus 1 third close parentheses

    open parentheses x minus 1 third close parentheses open parentheses x plus 1 third close parentheses is the required product of binomials.

    Factor the polynomial as the product of binomials.
    x squared minus 1 over 9

    Maths-General
    Ans :-  open parentheses x minus 1 third close parentheses open parentheses x plus 1 third close parentheses is the required product of binomials.
    Given , x squared minus 1 over 9
    Write text end text 1 over 9 text  as  end text open parentheses 1 third close parentheses squared text  then we get  end text x squared minus open parentheses 1 third close parentheses squared
    As  a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    Here a = x and b = 1 third

    x squared minus 1 over 9 equals open parentheses x minus 1 third close parentheses open parentheses x plus 1 third close parentheses

    open parentheses x minus 1 third close parentheses open parentheses x plus 1 third close parentheses is the required product of binomials.

    General
    Maths-

    A triangle having sides equal to 7cm, 24cm and 25cm forms a cone when revolved about 24cm side. What is the volume of a cone formed?

    We have given the dimensions of triangle having sides equal to 7cm, 24cm and 25cm
    It is revolved about 24 cm side
    Therefore, the cone formed will have dimensions as
    Height , h = 24 cm
    Radius , r = 7 cm
    So, the volume of cone = (1 third)πr2h

    = (1 third)(22 over 7)(7 x 7)(24)

    = 22 x 7 x 8

    = 1232 cm3
    Therefore, the correct option is b) 1232 cm3

    A triangle having sides equal to 7cm, 24cm and 25cm forms a cone when revolved about 24cm side. What is the volume of a cone formed?

    Maths-General
    We have given the dimensions of triangle having sides equal to 7cm, 24cm and 25cm
    It is revolved about 24 cm side
    Therefore, the cone formed will have dimensions as
    Height , h = 24 cm
    Radius , r = 7 cm
    So, the volume of cone = (1 third)πr2h

    = (1 third)(22 over 7)(7 x 7)(24)

    = 22 x 7 x 8

    = 1232 cm3
    Therefore, the correct option is b) 1232 cm3

    General
    Maths-

    What is the factored form of 4 x cubed plus 24 x squared plus 36 x space ?

    Hint :- factorize the given expression by taking out common elements and also using the required formulas .
    Ans:- 4x(x+3)(x+3) is the factorized form of the given expression.
    Explanation :-
    Given, 4 x cubed plus 24 x squared plus 36 x
    Taking out common factor 4 we get  4 open parentheses x cubed plus 6 x squared plus 9 x close parentheses
    Taking out common element x we get  4 left parenthesis x right parenthesis open parentheses x squared plus 6 x plus 9 close parentheses
    Splitting out 6x into 3x+3x we get 4 left parenthesis x right parenthesis open parentheses x squared plus 3 x plus 3 x plus 9 close parentheses equals 4 left parenthesis x right parenthesis left parenthesis x left parenthesis x plus 3 right parenthesis plus 3 left parenthesis x plus 3 right parenthesis right parenthesis
    Taking out x+3 common out we get 4 x left parenthesis x plus 3 right parenthesis left parenthesis x plus 3 right parenthesis
    As we get 4 x cubed plus 24 x squared plus 36 x equals 4 x left parenthesis x plus 3 right parenthesis left parenthesis x plus 3 right parenthesis
    ∴ 4x (x + 3)(x + 3) is the factorized form of the given expression.

    What is the factored form of 4 x cubed plus 24 x squared plus 36 x space ?

    Maths-General
    Hint :- factorize the given expression by taking out common elements and also using the required formulas .
    Ans:- 4x(x+3)(x+3) is the factorized form of the given expression.
    Explanation :-
    Given, 4 x cubed plus 24 x squared plus 36 x
    Taking out common factor 4 we get  4 open parentheses x cubed plus 6 x squared plus 9 x close parentheses
    Taking out common element x we get  4 left parenthesis x right parenthesis open parentheses x squared plus 6 x plus 9 close parentheses
    Splitting out 6x into 3x+3x we get 4 left parenthesis x right parenthesis open parentheses x squared plus 3 x plus 3 x plus 9 close parentheses equals 4 left parenthesis x right parenthesis left parenthesis x left parenthesis x plus 3 right parenthesis plus 3 left parenthesis x plus 3 right parenthesis right parenthesis
    Taking out x+3 common out we get 4 x left parenthesis x plus 3 right parenthesis left parenthesis x plus 3 right parenthesis
    As we get 4 x cubed plus 24 x squared plus 36 x equals 4 x left parenthesis x plus 3 right parenthesis left parenthesis x plus 3 right parenthesis
    ∴ 4x (x + 3)(x + 3) is the factorized form of the given expression.
    parallel
    General
    Maths-

    If the area of 1 face is 81 how much is the surface area of the whole cube?

    • Step 1:We have given area of one face of the cube.
    Area of face = 81
    • Step 2: For total surface area, find out the product of the square of side length by 6.
    Surface area =  6 (area of face)
                          =  6 (81)
                          =   486
    • Step 4: Therefore, the surface of the given cube is 486.
    • Therefore, the correct answer is option A) 486 .

    If the area of 1 face is 81 how much is the surface area of the whole cube?

    Maths-General
    • Step 1:We have given area of one face of the cube.
    Area of face = 81
    • Step 2: For total surface area, find out the product of the square of side length by 6.
    Surface area =  6 (area of face)
                          =  6 (81)
                          =   486
    • Step 4: Therefore, the surface of the given cube is 486.
    • Therefore, the correct answer is option A) 486 .
    General
    Maths-

    calculate the surface area of a cube with a side of 4 mm

    • Step 1:We have given the length of the side of the cube.

    Side = 4 mm

    • Step 2: Find the square of the length of the side of the cube.
    (Side)2= (4)2= 16 mm2
    • Step 3: For total surface area, find out the product of the square of side length by 6.
    Surface area = 6(side)2

    = 6(16)

    = 96 mm2

    • Step 4: Therefore, the surface area of the given cube is 96 mm2.
    • Therefore, the correct answer is option B) 96 mm2.

    calculate the surface area of a cube with a side of 4 mm

    Maths-General
    • Step 1:We have given the length of the side of the cube.

    Side = 4 mm

    • Step 2: Find the square of the length of the side of the cube.
    (Side)2= (4)2= 16 mm2
    • Step 3: For total surface area, find out the product of the square of side length by 6.
    Surface area = 6(side)2

    = 6(16)

    = 96 mm2

    • Step 4: Therefore, the surface area of the given cube is 96 mm2.
    • Therefore, the correct answer is option B) 96 mm2.
    General
    Maths-

    Ratio of volume of a cone to the volume of a cylinder for same base radius and
    same height is __________

    Solution :- Here is the activity for finding the volume of cone
    Let us take a cylinder  of height "h", base radius "r", and take 3 cones of height "h". Fill the cones with water and empty out one cone at a time


    Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.
    Volume of cone = (1/3) × Volume of cylinder
    = (1 third) × πr2h
    = (1 third)πr2h
    So the ratio of volume of cone to the volume of cylinder is 1:3
    Therefore , the correct option is b) 1:3

    Ratio of volume of a cone to the volume of a cylinder for same base radius and
    same height is __________

    Maths-General
    Solution :- Here is the activity for finding the volume of cone
    Let us take a cylinder  of height "h", base radius "r", and take 3 cones of height "h". Fill the cones with water and empty out one cone at a time


    Each cone fills the cylinder to one-third quantity. Hence, such three cones will fill the cylinder. Thus, the volume of a cone is one-third of the volume of the cylinder.
    Volume of cone = (1/3) × Volume of cylinder
    = (1 third) × πr2h
    = (1 third)πr2h
    So the ratio of volume of cone to the volume of cylinder is 1:3
    Therefore , the correct option is b) 1:3
    parallel
    General
    Maths-

    Find the Total surface area if the given dimensions are 6 cm,4cm, and 5 cm.

    Hint:- We have given three different dimensions ,
    Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
    where
    l → length of the cuboid
    b → breadth of the cuboid
    h → height of the cuboid
    Solution:-
    We will calculate the total surface area of a cuboid by using the following formula:
    text  T.S.A. of a cuboid  end text equals 2 cross times left square bracket 1 b plus b h plus h l right square bracket
    The dimensions of the given cuboid:
    Length, l = 4 cm
    Breadth, b = 5 cm
    Height, h = 6 cm
    By using the above formula of the total surface area of the cuboid, we get
    The total surface area of the given cuboid is,
    2 cross times left square bracket left parenthesis l b right parenthesis plus left parenthesis b h right parenthesis plus left parenthesis h l right parenthesis right square bracket
    2 cross times left square bracket left parenthesis 4 cross times 5 right parenthesis plus left parenthesis 5 cross times 6 right parenthesis plus left parenthesis 6 cross times 4 right parenthesis right square bracket
    2 cross times left square bracket 20 plus left parenthesis 30 right parenthesis plus left parenthesis 24 right parenthesis right square bracket
    2 cross times 74
    = 148 cm2
    Thus, the total surface area of a cuboid of dimensions 6 cm, 4 cm & 5 cm is 148 cm².
    The correct option is C)148 cm².
    Note:- In some examples it may be given the surface area and any two dimensions , then we have to adjust the formula such a that we will be able to find out the required value . For eg- If area , length and breadth is given the formula for height becomes
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator text  Area  end text over denominator 2 end fraction minus l b equals b h plus h l end cell row cell fraction numerator text  Area  end text over denominator 2 end fraction minus l b equals h left parenthesis b plus l right parenthesis end cell row cell h equals fraction numerator text  Area  end text over denominator 2 left parenthesis b plus l right parenthesis end fraction minus fraction numerator l b over denominator left parenthesis b plus l right parenthesis end fraction end cell end table

    Find the Total surface area if the given dimensions are 6 cm,4cm, and 5 cm.

    Maths-General
    Hint:- We have given three different dimensions ,
    Total Surface Area(TSA) of cuboid = 2[ lb + bh + hl ]
    where
    l → length of the cuboid
    b → breadth of the cuboid
    h → height of the cuboid
    Solution:-
    We will calculate the total surface area of a cuboid by using the following formula:
    text  T.S.A. of a cuboid  end text equals 2 cross times left square bracket 1 b plus b h plus h l right square bracket
    The dimensions of the given cuboid:
    Length, l = 4 cm
    Breadth, b = 5 cm
    Height, h = 6 cm
    By using the above formula of the total surface area of the cuboid, we get
    The total surface area of the given cuboid is,
    2 cross times left square bracket left parenthesis l b right parenthesis plus left parenthesis b h right parenthesis plus left parenthesis h l right parenthesis right square bracket
    2 cross times left square bracket left parenthesis 4 cross times 5 right parenthesis plus left parenthesis 5 cross times 6 right parenthesis plus left parenthesis 6 cross times 4 right parenthesis right square bracket
    2 cross times left square bracket 20 plus left parenthesis 30 right parenthesis plus left parenthesis 24 right parenthesis right square bracket
    2 cross times 74
    = 148 cm2
    Thus, the total surface area of a cuboid of dimensions 6 cm, 4 cm & 5 cm is 148 cm².
    The correct option is C)148 cm².
    Note:- In some examples it may be given the surface area and any two dimensions , then we have to adjust the formula such a that we will be able to find out the required value . For eg- If area , length and breadth is given the formula for height becomes
    table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em end attributes row cell fraction numerator text  Area  end text over denominator 2 end fraction minus l b equals b h plus h l end cell row cell fraction numerator text  Area  end text over denominator 2 end fraction minus l b equals h left parenthesis b plus l right parenthesis end cell row cell h equals fraction numerator text  Area  end text over denominator 2 left parenthesis b plus l right parenthesis end fraction minus fraction numerator l b over denominator left parenthesis b plus l right parenthesis end fraction end cell end table
    General
    Maths-

    Factor the given expression.
    9 x squared minus 100

    ANS :-  (3x-10)(3x+10) is the factorized form of the given expression.
    Given , 9 x squared minus 100
    Using square root and squaring on 9 and 100 . we get left parenthesis square root of 9 x right parenthesis squared minus left parenthesis square root of 100 right parenthesis squared
    using the formula a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    Here a equals square root of 9 x equals 3 x text  and  end text b equals square root of 100 equals 10
    Then 9 x squared minus 100 equals left parenthesis 3 x minus 10 right parenthesis left parenthesis 3 x plus 10 right parenthesis
    ∴ (3x - 10) (3x + 10) is the factorized form of the given expression.

    Factor the given expression.
    9 x squared minus 100

    Maths-General
    ANS :-  (3x-10)(3x+10) is the factorized form of the given expression.
    Given , 9 x squared minus 100
    Using square root and squaring on 9 and 100 . we get left parenthesis square root of 9 x right parenthesis squared minus left parenthesis square root of 100 right parenthesis squared
    using the formula a squared minus b squared equals left parenthesis a minus b right parenthesis left parenthesis a plus b right parenthesis
    Here a equals square root of 9 x equals 3 x text  and  end text b equals square root of 100 equals 10
    Then 9 x squared minus 100 equals left parenthesis 3 x minus 10 right parenthesis left parenthesis 3 x plus 10 right parenthesis
    ∴ (3x - 10) (3x + 10) is the factorized form of the given expression.
    General
    Maths-

    Factor the polynomial as the product of binomials.
    x squared plus x plus 1 fourth

    Ans :- open parentheses x plus 1 half close parentheses open parentheses x plus 1 half close parentheses is the required product of binomials.
    Given , x squared plus x plus 1 fourth
    Write1 fourth text  as  end text open parentheses 1 half close parentheses squared text  and  end text x text  as  end text 2 open parentheses 1 half close parentheses left parenthesis x right parenthesis then we get x squared plus 2 open parentheses 1 half close parentheses x plus open parentheses 1 half close parentheses squared
    As a squared plus 2 a b plus b squared equals left parenthesis a plus b right parenthesis squared
    Here a = x and b =  1 half
    x+ x + 1 fourth = (x +1 half)2 = (x + 1 half) (x +1 half)
    ∴ (x+1 half)(x+1 half) is the required product of binomials.

    Factor the polynomial as the product of binomials.
    x squared plus x plus 1 fourth

    Maths-General
    Ans :- open parentheses x plus 1 half close parentheses open parentheses x plus 1 half close parentheses is the required product of binomials.
    Given , x squared plus x plus 1 fourth
    Write1 fourth text  as  end text open parentheses 1 half close parentheses squared text  and  end text x text  as  end text 2 open parentheses 1 half close parentheses left parenthesis x right parenthesis then we get x squared plus 2 open parentheses 1 half close parentheses x plus open parentheses 1 half close parentheses squared
    As a squared plus 2 a b plus b squared equals left parenthesis a plus b right parenthesis squared
    Here a = x and b =  1 half
    x+ x + 1 fourth = (x +1 half)2 = (x + 1 half) (x +1 half)
    ∴ (x+1 half)(x+1 half) is the required product of binomials.

    parallel

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