Question

Find the cube root of 13824 and 15625 by prime factorization method

Answer 1

Answer:

filledbookmark

USE APP

Sign in

Questions & Answers

CBSE

Mathematics

Grade 8

Cube root through prime factorisati...

Question

Answers

Related Questions

Find the cube root of 13824 by the method of prime factorization.

A. 24B. 18C. 12D. 36

Answer

VerifiedVerified

35.3K+ Views

2 Likes

Hint- In order to solve such a question of finding cube root by prime factorization method, first find the prime factorization of the number and further make the triplet of factors.

Complete step-by-step solution -

Given number: 13824

In order to find the prime factorization of the number, we continuously divide the number with prime numbers.

Prime factorization of number 13824 is:

13824=2×2×2×2×2×2×2×2×2×3×3×3

Further we make the triplet of factors:

13824=(2×2×2)×(2×2×2)×(2×2×2)×(3×3×3)

Further simplifying the RHS and writing it in the form of a cube.

⇒13824=23×23×23×33⇒13824=29×33

Now we will proceed with finding the cube root

⇒(13824)13=(29×33)13⇒(13824)13=[(23×3)3]13⇒(13824)13=(23×3)3×13 [∵(am)n=am×n]⇒(13824)13=23×3⇒(13824)13=8×3=24

Hence, the cube root of 13824 is 24.