Question

find the smallest number by which the given number must be multiplied so that the prodect is a perfect square. (7688)​

Answer 1

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First of all find out the prime factorization of 7688.

Prime Factorization of 7688 = 2 × 2 × 2 × 31 × 31

The only number in the above which has no pair is 2.

So, we have to multiply 7688 by 2 to get the perfect square.

⇒ 7688 × 2 = 15376

15376 is a perfect square.

Let us check it.

Take square root of 15376.

⇒ √15376 = 124

Square root of 15376 is 124.

Answer 2

First of all find out the prime factorization of 7688.

Prime Factorization of 7688 = 2 × 2 × 2 × 31 × 31

The only number in the above which has no pair is 2.

So, we have to multiply 7688 by 2 to get the perfect square.

⇒ 7688 × 2 = 15376

15376 is a perfect square.

Let us check it.

Take square root of 15376.

⇒ √15376 = 124

Square root of 15376 is 124