Question

find the cube root of 729​

Answer 1

Answer:

The cube root of 729, denoted as 3√729, is a value which after getting multiplied by itself thrice gives the original value. This is the usual definition of the cube root of a number. Let us say, ‘n’ is the value of 3√729, then n × n × n = n3 = 729. Since 729 is a perfect cube, we will use the prime factorisation method, to get the cube root easily. Therefore, we need to find the value of n here

Let us understand it in a step by step procedure.

Step 1: Find the prime factors of 729

729 = 3 × 3 × 3 × 3 × 3 × 3

Step 2: Clearly, 729 is a perfect cube. Here we will be using laws of exponents.

729 = 36 [am × an = am+n]

729 = [32]3 [(am)n = amn]

729 = 93

Step 3: Now, we will apply cube root to both the sides of the above expression to take out the factor as a single term, which is in cubes.

3√729 = 3√(93)

So, here the cube root is cancelled by the cube of 9.

Hence, 3√729 = 9

Finding the cube root of perfect cubes up to three-digit numbers is easy if we memorise the below-given table.