Using prime factorisation, find the following is a perfect cube : 729

Solution:

Given, the number is 343.

We have to determine if 343 is a perfect cube 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, 729 = 3 × 3 × 3 × 3 × 3 × 3

We observe that the prime factor 3 occurs in pairs.

Cube of 9 is 729.

Therefore, 729 is a perfect cube.

✦ Try This: Using prime factorisation, find the following is a perfect cube : 849

☛ Also Check: NCERT Solutions for Class 8 Maths

NCERT Exemplar Class 8 Maths Chapter 3 Problem 92 (c)

Using prime factorisation, find the following is a perfect cube : 729

Summary:

By checking 729 using prime factorisation, it is clear that 729 is a perfect cube.

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