Maths-
General
Easy

Question

Represent  square root of 2and square root of 3 on the number line

hintHint:

Hint:
A number line is a straight line with numbers placed at equal intervals or segments along its length. Some square roots are irrational numbers and irrational numbers cannot be directly plotted on the number line so we use some geometrical techniques to plot irrational numbers on the number line.
 

The correct answer is: Represented on the number line as


    Step 1: Draw a number line and mark point O. This point represents 0 on the number line. Numbers to the left of O are negative numbers and numbers to the right of O are positive numbers.
    Step 2: Mark a point A on the number line such that OA = 1 unit
    Step 3: Draw a line AB such that AB is perpendicular to the number line and AB = 1 unit. This results in a right-angled triangle OAB.
    Step 4: Now, join OB
    Step 5: By using Pythagoras Theorem, the length of OB can be found as
    OB equals square root of 1 squared plus 1 squared end root equals 2 text  units  end text
    Step 6: With O as centre and OB as radius, draw an arc on the number line and mark the point as D. The point D represents  square root of 2on the number line.
    Step 7: Now,draw a line BC perpendicular to OB such that BC = 1 unit
    Step 7: Then join OC
    Step 8: OBC is a right-angled triangle. By using Pythagoras theorem, we have
    O C equals square root of 2 squared plus 1 squared end root equals 3 text  units  end text
    Step 9: With O as centre and OC as radius, draw an arc on the number line and mark the point as E. The point E represents square root of 3 on the number line.
    Final Answer:
    Hence,  square root of 2 and square root of 3 can be represented on the number line as

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