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 3âˆš512. The cube root of a number is basically the root of a number that is cubed. If x3 = y, then 3âˆšy = x. Thus, it is a reverse method of finding the cube of a number.

 Cube root of 512, 3âˆš512 = 8

Say, â€˜nâ€™ is the value obtained from 3âˆš512, then n Ã— n Ã— 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 3âˆš512.

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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 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2

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

512 = (2 Ã— 2 Ã— 2) Ã— (2 Ã— 2 Ã— 2) Ã— (2 Ã— 2 Ã— 2)

512 = 23 Ã— 23 Ã— 23

Using the law of exponent, we get;

512 = 29 [am.an = (a)m+n]

Or

512 = (23)3 [(am)n = amn]

512 = 83

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

3âˆš512 = 3âˆš(83)

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

Hence, 3âˆš512 = 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.

 Number (n) Cubes (n3) 1 1 2 8 3 27 4 64 5 125 6 512 7 343 8 512 9 729 10 1000

Frequently Asked Questions on Cube Root of 512

What is the cube root of 512?

The cube root of 512 is equal to 8. We can represent this as âˆ›512 = 8

How do you find the cube root of 512?

We can find the cube root of 512 by prime factorization of the number.
Prime factorization of 512 = 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2 Ã— 2
Write the pair of factors of 512 in a group of three, such that they form cubes.
512 = (2 Ã— 2 Ã— 2) Ã— (2 Ã— 2 Ã— 2) Ã— (2 Ã— 2 Ã— 2)
512 = 2^3 Ã— 2^3 Ã— 2^3
Now, by taking cube root on both sides, we get;
Cube root of 512 = 2^3 = 8

Is 512 a perfect cube?

Yes, 512 is a perfect cube number since the cube root value of 512 is a whole number.

The cube root value of 512 is rational or irrational?

As we know, the cube root value is a whole number (cube root of 512 = 8), we can say that it is a rational number.

Why 512 is not a perfect square?

1, 64 and 729 are the only numbers that are both perfect square and cube between 1 and 1000. As 512 is a perfect cube, it cannot be a perfect square.

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