Question

by which smallest number should we divide the following number to make them perfect square find the square root of the perfect square 9680​

Answer 1

Step-by-step explanation:

Resolving 9680 into prime factors :-

9680 = 2×2×2×2×11×11×5 .

Hence the required number is 5

New number = (9680 ÷ 5) = 1336

√1936 = 44

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Answer 2

• 5 is the smallest number by which the number 9680 must be divided to make a perfect square

• The square root of the perfect square = 44

Given :

The number 9680

To find :

• The smallest number by which we divide the number 9680 to make a perfect square

• The square root of the perfect square

Concept :

Step : I - Firstly express the given number as a product of prime factor by using prime

factorisation

Step : II - Make the pair of similar factors such that the both factors in each pair are equal.

Step : III - Take one factor from each pair.

Step : IV - If no factor is left over in grouping (pairs) then the number is perfect square

otherwise not

Solution :

Step 1 of 3 :

Prime factorise the given number

Here the given number is 9680

9680 = 2 × 2 × 2 × 2 × 11 × 11 × 5

∴ 9680 = 2² × 2² × 11² × 5

Step 2 of 3 :

Find the smallest number by which the number 9680 must be divided to make a perfect square

Since the factor 5 does not have pair

So we need to divide the number 9680 by 5 to make a perfect square

Hence 5 is the smallest number by which the number 9680 must be divided to make a perfect square

Step 3 of 3 :

Find the square root of the perfect square

The perfect square number = 9680/5 = 1936

Hence the square root of the perfect square

= √1936

= 44

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