# By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient.

**Solution:**

Given, the number is 216.

We have to find the smallest number by which 216 should be __divided__ so that the quotient is a __perfect square__ and the __square root__ of the quotient.

__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, 216 = 2 × 2 × 2 × 3 × 3 × 3

We observe that 2 and 3 occur without a pair.

216 must be divided by 2 × 3

2 × 3 = 6

So, 216 / 6 = 36

This implies the quotient is a perfect square.

Therefore, the smallest number by which 216 must be divided is 6.

Square root is an inverse operation of a square.

So, √36 = √(6)²

= 6

Therefore, the square root of the quotient is 6.

**✦ Try This: **By what smallest number should 729 be divided so that the quotient is a perfect square. Also find the square root of the quotient.

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

**NCERT Exemplar Class 8 Maths Chapter 3 Problem 101**

## By what smallest number should 216 be divided so that the quotient is a perfect square. Also find the square root of the quotient

**Summary:**

The smallest number by which 216 should be divided so that the quotient is a perfect square is 6. The square root of the quotient is 6.

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