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# Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

**Solution:**

Given, the number is 176.

We have to determine if 176 is a __perfect square__ or not.

__Prime factorization__ is a way of expressing a number as a product of its prime __factors__.

A prime number is a number that has exactly two factors, 1 and the number itself.

Using prime factorisation,

So, 176 = 2 × 2 × 2 × 2 × 11

We observe that 11 occurs without a pair.

Therefore, 176 is not a perfect square.

We have to determine the smallest number by which 176 should be __multiplied__ to get a perfect square.

176 should be multiplied by 11.

So, 176 × 11 = 1936

Factors of 1936 = 2 × 2 × 2 × 2 × 11 × 11

= √1936

= √(2² × 2² × 11²)

= 2 × 2 × 11

= 44

Therefore, the smallest number to be multiplied is 11.

**✦ Try This: **Is 396 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square.

**☛ Also Check:** NCERT Solutions for Class 8 Maths

**NCERT Exemplar Class 8 Maths Chapter 3 Problem 98**

## Is 176 a perfect square? If not, find the smallest number by which it should be multiplied to get a perfect square

**Summary:**

176 is not a perfect square. The smallest number by which 176 should be multiplied to get a perfect square is 11.

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