Question

Find the smallest number by which the 9680 should be multiplied so that the product becomes a perfect square.​

Answer 1

Answer:

the smallest number is five

Answer 2

5 is the smallest number by which the 9680 should be multiplied so that the product becomes a perfect square.

Given :

The number 9680

To find :

The smallest number by which the 9680 should be multiplied so that the product becomes a 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 2 :

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 2 :

Find the smallest number by which the 9680 should be multiplied so that the product becomes a perfect square.

Since the factor 5 does not have pair

So in order to make a pair for 5 we need to multiply the number by 5

Hence 5 is the smallest number by which the 9680 should be multiplied so that the product becomes a perfect square.

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