Cube Root of 512

Cube Root of 512 is 8. We define cube root as the number which when multiplied by itself twice result in the original number, i.e. 8 when multiplied by itself twice gets 512, i.e. 8 × 8 × 8 = 512.

In radical form of the cube root of 512 is represented as, ³√(512), and exponential form for the same is (512)^1/3.

In this article, we will learn to find the cube root of 512 by various methods and some solved examples related to the same.

What is Cube Root of 512?

Cube Root of 512 is a value that when multiplied by itself three times results in 512. Now we all know that, 512 = 8 × 8 × 8, so it is clear that multiplying 8 three times results in 512 thus, cube root of 512 is 8.

Mathematically, if x is the cube root of 512, it can be represented as:

x³ = 512,

⇒ x = (512)^1/3

⇒ x = 8

i.e. cube root of 512 is written as,

∛(512) = 8

Cube Root Definition

Cube root of a number is a value, when multiplied by itself twice and that gives the original number. ∛(x) symbol represent cube root of any number x

Cube Root Calculator

To find the cube root of any number, you can use the following calculator:

How to Find Cube Root of 512?

To find the cube root of 512 various methods can be used that are given below:

• Cube Root of 512 by Successive Subtraction Method
• Cube Root of 512 by Prime Factorization Method

Now let’s find cube root of 8 using the above mentioned methods.

Cube Root of 512 by Successive Subtraction

Cube roots of any number is found by subtracting the following numbers by successive subtraction of numbers: 1, 7, 19, 37, 61 , 91, 127, 169, 217, 271, 331, 397, . . .

We can use this method to find cube root of 512 as,

• 512 − 1 = 511
• 511 − 7 = 504
• 504 − 19 = 485
• 485 − 37 = 448
• 448 − 61 = 387
• 387 − 91 = 296
• 296 − 127 = 169
• 169 − 169 = 0

As soon as we get zero we have to count the number of subtraction steps which in turn gives us the value of cube root. in this case we have perform 8 subtraction steps so cube root of 512 is 8, i.e. 512 = (8)³.

Cube Root of 512 by Prime Factorization Method

512 is divided successively by prime numbers beginning at 2 until we are unable to divide it any more in order to determine the prime factorization of 512:

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

⇒ 512 = 2³ × 2³ × 2³

⇒ ∛(512) = 2 × 2 × 2 = 8

Therefore, the cube root of 512 is 8 is resolved by the prime factorization method.

Is Cube Root of 512 a Rational or Irrational Number?

If any number is expressed in the form of p/q, where q is not equal to 0, then the numbers is called rational number. Here we see that cube root of 512 is 8, i.e. represented as, 8/1 a rational number. So

(512)^1/3 = 8/1

Is a rational number.

Examples on Cube Root of 512

Example 1: Simplify ∛(512) × ∛(-512)

Solution

We know,

• ∛(512) = 8
• ∛(-512) = -8

Hence, ∛(512) × ∛(-512) = 8 × (-8) = -64

Example 2: Simplify ∛(512) + ∛(-512)

Solution

We know,

• ∛(512) = 8
• ∛(-512) = -8

Hence, ∛(512) + ∛(-512) = 8 + (-8) = 8 – 8 = 0

Example 3: Simplify ∛(512) – ∛(-512)

Solution

We know,

• ∛(512) = 8
• ∛(-512) = -8

Hence, ∛(512) – ∛(-512) = 8 – (-8) = 8 + 8 = 16

Practice Questions

Q1: Calculate Cube Root of (1/512).

Q2: Calculate Cube Root of (-512).

Q3: Find Cube Root of,

• 8
• 27
• 62
• 125

Cube Root of 512: FAQs

What is the Value of the Cube Root of 512?

The cube root of 512 is 8.

Is the cube root of 512 a rational number?

Yes, the cube root of 512 is a rational number because it can be expressed in the form of two integers.

What is the cube root of 512 in radical form?

The cube root of 512 can be expressed as ∛ (512) in radical form.

What methods are used to find the cube root of 512?

For finding the cube root of 512, we use

• Successive Subtraction Method
• Prime Factorization Method

What is the cube root of negative 512?

The cube root of (-512) is (-8).

Is 512 a Perfect Cube?

Cube root of 512 is 8, which is a whole number, therefore, 512 is a perfect cube.