Question

Find the Smallest Number by which 22050 must be multiplied so as to make it a perfect square

Answer 1

2 os multiplied to 22050 to make it perfect square

Answer 2

2 is the smallest number by which 22050 must be multiplied so as to make it a perfect square

Given :

The number 22050

To find :

The smallest number by which 22050 must be multiplied so as to make it 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 22050

22050 = 2 × 3 × 3 × 5 × 5 × 7 × 7

∴ 22050 = 2 × 3² × 5² × 7²

Step 2 of 2 :

Find the smallest number by which 22050 must be multiplied so as to make it a perfect square

Since the factor 2 does not have pair

So we need to multiply the number 22050 by 2 to make a perfect square

Hence 2 is the smallest number by which 22050 must be multiplied so as to make it a perfect square

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