How to find if the given number is a perfect cube?

If the prime factors of a number are grouped in triples of equal factors, then that number is called a perfect cube.

**Examples to find if the given number is a perfect cube:
1. Find out if the following are perfect cubes.**

(i) 250

(ii) 5832

**Solution: **

Resolving 250 as the product of prime factors

250 = 2 × __5 × 5 × 5__

Since 2 does not exist in product of triples.

Therefore, 250 is not a perfect cube.

** (ii) 5832**

**Solution: **

Resolving 5832 as the product of prime factors

5832 = __2 × 2 × 2__ × __3 × 3 × 3__ × __3 × 3 × 3__

Since, they are grouped in triples.

Therefore, 5832 is a perfect cube.

**2. Find the smallest number by which 1944 must be multiplied so that the product is a perfect cube.
Solution: **

Resolving 1944 as the product of prime factors

1944 = __2 × 2 × 2__ × __3 × 3 × 3__ × 3 × 3

In order to make 1944 a perfect cube, it must be multiplied by 3.

**3. Find the smallest number by which 4394 must be divided so that the quotient is a perfect cube.
Solution: **

Resolving 4394 as the product of primes

4394 = 2 × __13 × 13 × 13__

In order to make 4394 a perfect cube, it must be divided by 2, so that the quotient is 2197.

● **Cube and Cube Roots**

**To Find if the Given Number is a Perfect Cube**

**Method for Finding the Cube of a Two-Digit Number**

● **Cube and Cube Roots - Worksheets**

**Worksheet on Cube and Cube Root**

**8th Grade Math Practice**** ****From To Find if the Given Number is a Perfect Cube to HOME PAGE**

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