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 81/3. 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?

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, ∛8 = 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

More Articles on Cube Root of a Number:

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.


Frequently Asked Questions on Cube Root of 8

Q1

What is the value of ∛8?

The value of cube root of 8, ∛8, is 2.

Q2

What is the cube of cube root of 8?

The cube of cube root of 8 is 8.

i.e. (∛8)3 = 8 (On cancelling cube and cube root).

Q3

Is 8 a perfect cube number?

Yes, 8 is a perfect cube number, as it can be expressed in the form of three equal integers, i.e. 8 = 2×2×2.

Q4

Is the cube root of 8 an irrational number?

No, the cube root of 8 is not an irrational number. It is a rational number as ∛8 can be expressed as 2/1.

Q5

What is the value of 4 plus the cube root of 8?

The value of 4 plus the cube root of 8 is 6.

i.e. 4 + ∛8 = 4 + 2 = 6.

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