Question

How to find the cube root of 74088 with prime factorisation method.

Answer 1

find the prime factors of 74088
74088/2
37044/2
18522/2
9261/3
3087/3
1029/3
343/7
49/7
7/7
1
note down the factors
2*2*2*3*3*3*7*7*7=74088
now make groups of 3 same no.s(for eg.2*2*2)
and just write the groped no. once.(for eg. for2*2*2=2)
so,
2*3*7=42
thus,cube root of 74088 is 42

Answer 2

Given: A number 74088

To find: Cube root of 74088 using prime factorization method

Solution: Using prime factorization method, 74088 can be expressed as:

74088 = 2 × 2 × 2 × 3 × 3 × 3 × 7 × 7 × 7

Since 74088 can be expressed as the product of pairs of equal prime factors, its cube root is 2 × 3 × 7 (Product of a number taken from each pair of equal prime factors) i.e. 42.

⇒ $\sqrt[3]{74088} = 42$

Hence, the cube root of 74088 is 42.