Cube Root of 8

In Mathematics, the cube root of 8, also denoted as ∛8, is the real solution of the equation x³ = 8. The cube root of 8 in radical form is ∛8. It is also expressed as 8^1/3. The number 8 is a perfect cube number and it is a whole number. In this article, we are going to learn the value of cube root of 8. We will also look at the prime factorization method to find the value of ∛8 with examples, and a complete explanation.

Table of Contents:

• What is the Value of Cube Root of 8?
• Cube Root of 8 by Prime Factorization Method
• Is the Cube Root of 8 a Rational Number?
• Examples
• FAQs

What is the Value of Cube Root of 8?

The cube root of 8, ∛8, is a number that, when multiplied by itself three times results in the original number 8. We know that 8 is a perfect cube number, and hence the value of cube root of 8 is 2.

Cube Root of 8 by Prime Factorization Method

Since 8 is a perfect cube number, the value of cube root of 8 is found using the prime factorization method. Follow the below steps to find the cube root of 8.

We know that the prime factorization of 8 is 2×2×2.

Thus, ∛8 = ∛(2×2×2)

∛8 = ∛(2)³

Now, cancel out cube and cube root, we get

∛8 = 2

Hence, ∛8 = 2.

Is the Cube Root of 8 a Rational Number?

Yes, the cube root of 8 is a rational number. Since the value of ∛8 can be expressed in the form of p/q, (i.e.) 2/1, the cube root of 8 is considered as a rational number.

Video Lesson on Finding Cube Roots

Solved Examples

Example 1:

What is the value of ∛8 + 10?

Solution:

Given: ∛8 + 10.

As we know, the value of cube root of 8 is 2.

Therefore,

∛8 + 10 = 2+10

∛8 + 10 = 12.

Hence, the value of ∛8 + 10 is 12.

Example 2:

Find the value of a, if 2a + ∛8 = 12.

Solution:

Given: 2a + ∛8 = 12

We know that ∛8 = 2.

Substitute the value in the given equation,

2a + 2 = 12

2a = 12 – 2

2a = 10

a = 10/2

a = 5

Therefore, the value of a is 5.

Example 3:

Solve the equation x³ – 8 = 0.

Solution:

Given equation: x³ – 8 = 0

Thus, x³ = 8

Now, take cube root on both sides of the equation,

∛x³ = ∛8

On removing cube and cube root on the left-hand side of the equation, we get

x = ∛8

Hence, x = 2 [Since, ∛8 = 2]

Therefore, the value of x is 2.