Cube Root of 512

The cube root of 512 is a value that results in its original number after getting multiplied by itself, three-times. It is denoted as ³√512. The cube root of a number is basically the root of a number that is cubed. If x³ = y, then ³√y = x. Thus, it is a reverse method of finding the cube of a number.

Say, ‘n’ is the value obtained from ³√512, then n × n × n = n³ = 512 (as per the definition of a cube). Since 512 is a perfect cube, we will use here the prime factorisation method, to get the cube root easily. Learn more here, to calculate the value of ³√512.

Also, check:

• Cube Root Of Unity
• Square Root And Cube Root
• How to find cube root
• Cube root table

How to Find Cube Root of 512

By the use of the prime factorisation method, we can find the prime factors of the given number. Now when we take the cube root of the given number, the identical or similar factors can be paired in a group of three. Hence, we will get the cubes of prime factors. Now, on applying the cube root it gets cancelled by the cubed number present within it.

Let us understand it step by step.

Step 1: Find the prime factors of 512

512 = 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2

Step 2: Pair the factors of 512 in a group of three, such that they form cubes.

512 = (2 × 2 × 2) × (2 × 2 × 2) × (2 × 2 × 2)

512 = 2³ × 2³ × 2³

Using the law of exponent, we get;

512 = 2⁹ [a^m.aⁿ = (a)^m+n]

Or

512 = (2³)³ [(a^m)ⁿ = a^mn]

512 = 8³

Step 3: Now, we will apply cube root on both sides to take out the factor (in cubes) as a single term.

³√512 = ³√(8³)

So, here the cube root is eliminated by the cube of 8.

Hence, ³√512 = 8

Video Lesson on Finding Cube Roots

Cube Table:

Below is the table of cubes of 1 to 10 numbers to find the cube root easily.