Question
What is the smallest number by which 3600 be divided to make it a perfect cube.
- 450
- 445
- 440
- 430
Hint:
A number is considered to be a perfect cube if it can be multiplied by itself 3 times. Consider the example of 27. 27 can be expressed in terms of 3 raised to power 3, which is:
We have given the number 3600 and the options are 450, 440, 445, and 430 so the final answer will be in terms of a perfect cube.
The correct answer is: 450
Now, we have given the number 3600 and the options are 450, 440, 445, and 430 and we have to find the smallest number by which 3600 be divided to make it a perfect cube.
So, lets divide the given number i.e. 3600 by all the four options:
First number is 450, so:
Here 8 is the perfect cube of 2.
Second number is 440, so:
Here 8.1818 is a decimal number and its not a perfect cube.
Third number is 445, so:
Here 8.089 is a decimal number and its not a perfect cube.
Fourth number is 430, so:
Here 8.372 is a decimal number and its not a perfect cube.
After dividing by all the numbers we can say that 3600 should be divided by 450 so that the value obtained is 8 which is the perfect cube of 2.
In this question we have given the term 3600 which has to be divided by a number such that its answer should be the perfect cube. Hence we divided by all the given options and found that dividing by 450 results in the perfect cube, that is 8.
Another method is by factorisation, we can find the factors of 3600:
The prime factorization of 3600 shows that factor 2 is repeated four times whereas the other factors are reproduced less than 3 times. A repeating factor that occurs three times must exist for a perfect cube.
So 3600 must be divided by 2×3×3×5×5 to get 2x2x2=8 as the perfect cube.
Related Questions to study
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So, we have given the volume of cube as 
. So we found out the dimension of cube first and substituted the value of dimension in the formula of total surface area of cube and we found out the total surface area of cube is 
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The volume of a cube is 343 cm3. Its surface area would be:
So, we have given the volume of cube as . So we found out the dimension of cube first and substituted the value of dimension in the formula of total surface area of cube and we found out the total surface area of cube is .
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Here we have to find out the number of students in the class. The amount paid by every student is equal to the number of students in the class. So we used the concept of square root and found that the total number of students are 77 in the class.
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What should come in place of both x in the equation:
In this question, we have given the expression with two values with square root and we have to find the value of x. We used the cross multiplication technique to solve this expression. After cross multiplying we used the square root method to find the value of x which came out to be 12.
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Here we have to find out the number of rows to plant trees. The number of plants in a row should be equal to the number of rows. So we used the concept of square root and found that the total number of rows will be 45 and the plants in 1 row will be 45.
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Here in this question, we have given that while packing 85 books in each bag, 9 bags were not filled completely. Another condition is given as while packing 58 books in each bag, 13 bags were not enough to pack all the books. It is also provided that he was able to pack the books in M bags each having M books. So via the square root concept, we found out that there are 784 books in total.
Peter had some books in his library. He tried packing them in bags in various ways. While packing 85 books in each bag, 9 bags were not filled completely. Also, while packing 58 books in each bag, 13 bags were not enough to pack all the books. But in the end he was able to pack the books in M bags each having M books. How many books did Peter have?
Here in this question, we have given that while packing 85 books in each bag, 9 bags were not filled completely. Another condition is given as while packing 58 books in each bag, 13 bags were not enough to pack all the books. It is also provided that he was able to pack the books in M bags each having M books. So via the square root concept, we found out that there are 784 books in total.
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In this question, the area of one side is given as 5 square cm, so the total surface area of the cube can be calculated by just multiplying 6 by the area given as there are 6 faces in the cube.
Alternate method is that we can just add 5 cm square for 6 times which will result in total surface area of cube.
Find the surface area of the cube if the area of one face of the cube is 5 square units
In this question, the area of one side is given as 5 square cm, so the total surface area of the cube can be calculated by just multiplying 6 by the area given as there are 6 faces in the cube.
Alternate method is that we can just add 5 cm square for 6 times which will result in total surface area of cube.
Find the surface area of the cube if the area of one face of the cube is 5 square units
In this question, the area of one side is given as 5 square cm, so the total surface area of the cube can be calculated by just multiplying 6 by the area given as there are 6 faces in the cube.
Alternate method is that we can just add 5 cm square for 6 times which will result in total surface area of cube.
Find the surface area of the cube if the area of one face of the cube is 5 square units
In this question, the area of one side is given as 5 square cm, so the total surface area of the cube can be calculated by just multiplying 6 by the area given as there are 6 faces in the cube.
Alternate method is that we can just add 5 cm square for 6 times which will result in total surface area of cube.
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A square garden has an area of 225 square feet. How much fencing would a gardener need to buy to place it around the garden?
In this question, we have given that a square garden has an area of 225 square feet, and the dimension was supposed to be found. We used the concept of square root where the area was already given and with the help of that we calculated the dimension of fencing of one side and multiplied by 4 to get the total dimension of the squared garden which came out to be 60 feet.
A square garden has an area of 225 square feet. How much fencing would a gardener need to buy to place it around the garden?
In this question, we have given that a square garden has an area of 225 square feet, and the dimension was supposed to be found. We used the concept of square root where the area was already given and with the help of that we calculated the dimension of fencing of one side and multiplied by 4 to get the total dimension of the squared garden which came out to be 60 feet.
In this question, we have given 4 models out of which we have to find the perfect model which can represent 4x4. So out of all the 4 models, the first model seems to be the perfect fit for the given measurement. Here the square function is the concept used.
In this question, we have given 4 models out of which we have to find the perfect model which can represent 4x4. So out of all the 4 models, the first model seems to be the perfect fit for the given measurement. Here the square function is the concept used.
In this question we have given a model which has an area of 36 square units. We have to find the side of the square and hence we used the concept of square function. Through this, we found out the dimension of the given model is 6 units, or more specifically 
.
In this question we have given a model which has an area of 36 square units. We have to find the side of the square and hence we used the concept of square function. Through this, we found out the dimension of the given model is 6 units, or more specifically .
The area of a square is 144 square meters. Find the perimeter of the square.
In this question, we have given the area of the square and we have to find the perimeter. So we used the concept of a square function and using that we first found out the side of the square which was found to be 12 meters and then we multiplied it by 4 which came out to be 48 meters as perimeter of the square.
The area of a square is 144 square meters. Find the perimeter of the square.
In this question, we have given the area of the square and we have to find the perimeter. So we used the concept of a square function and using that we first found out the side of the square which was found to be 12 meters and then we multiplied it by 4 which came out to be 48 meters as perimeter of the square.
