Using prime factorisation, find the cube root of 512.

Solution:

Given, the number is 512.

We have to determine the cube root of 512 using prime factorisation.

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, 512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

We observe that 2 occur in pairs.

Cube root is an inverse operation of the cube.

So, ∛4761 = ∛( 2³ × 2³ × 2³)

= 2 × 2 × 2

= 8

Therefore, the cube root of 512 is 8.

✦ Try This: Using prime factorisation, find the cube root of 125.

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 3 Problem 97 (a)

Using prime factorisation, find the cube root of 512

Summary:

Using prime factorisation, the cube root of 512 is 8.

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