# By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.

**Solution:**

Given, the number is 3600.

We have to find the smallest number by which 3600 should be __multiplied__ so that the quotient is a perfect cube and the __cube 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, 3600 = 2 × 2 × 2 × 2 × 3 × 3 × 5 × 5

We observe that 2 occurs once and 3,5 occur twice.

3600 must be multiplied by 2 × 2 × 3 × 5 to make it a perfect cube.

2 × 2 × 3 × 5 = 60

So, 3600 × 60 = 216000

Therefore, the smallest number by which 3600 must be multiplied is 60.

Cube root is an inverse operation of a cube.

216000 = 2 × 2 × 2 × 2 × 2 × 2 × 3 × 3 × 3 × 5 × 5 × 5

So, ∛216000 = ∛(2³ × 2³ × 3³ ×5³)

= 2 × 2 × 3 × 5

= 60

Therefore, the cube root of the quotient is 60.

**✦ Try This: **By what smallest number should 2500 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient.

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

**NCERT Exemplar Class 8 Maths Chapter 3 Problem 102**

## By what smallest number should 3600 be multiplied so that the quotient is a perfect cube. Also find the cube root of the quotient

**Summary:**

The smallest number by which 3600 should be multiplied so that the quotient is a perfect cube is 60. The cube root of the quotient is 60.

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