Cube root of 27 by the prime factorisation method

When the number is multiplied three times by itself, the resultant number is the cube of that number and the cube root is the inverse of the cube i.e., the number which is multiplied three times by itself is the cube root. In this article, we are going to learn about the cube root of 27 and the prime factorisation method to find the cube root of 27.

Cube root

Introduction

The cube of a number is equal to the number obtained by multiplying three times by itself. For example the cube of 2 is 8( as 2 x 2 x 2 =8). Similarly, the cube root of a number is that factor that is multiplied three times by itself to obtain that number. For example, the cube root of 8 is 2 (as 2, when multiplied three times by itself, gives 8).

Method of finding the cube root

PRIME FACTORISATION METHOD

The prime factorization method is the method of finding the cube root by using its prime factors. The following steps are to be followed to find the cube root of a number by using the prime factorization method-.

~Choose the number of which the cube root is to be found, Consider the number 27.

~ Divide 27 with the lowest prime number. Once the number ceases to be divisible by that first chosen prime number, choose another higher prime number and continue the process until the quotient thus obtained also results in a prime number.

~Arrange the factors in groups of threes. Here, 27 – 3 x 3 x 3, which is 3³.

~ Pick one number from each group and find their product, the product thus obtained is equal to the cube root of the number which is =  ∛27=  ∛3³ = 3.