A day full of math games & activities. Find one near you.

Cube Root of 135

The value of the cube root of 135 rounded to 6 decimal places is 5.129928. It is the real solution of the equation x³ = 135. The cube root of 135 is expressed as ∛135 or 3 ∛5 in the radical form and as (135)^⅓ or (135)^0.33 in the exponent form. The prime factorization of 135 is 3 × 3 × 3 × 5, hence, the cube root of 135 in its lowest radical form is expressed as 3 ∛5.

Cube root of 135: 5.12992784
Cube root of 135 in Exponential Form: (135)^⅓
Cube root of 135 in Radical Form: ∛135 or 3 ∛5

1.	What is the Cube Root of 135?
2.	How to Calculate the Cube Root of 135?
3.	Is the Cube Root of 135 Irrational?
4.	FAQs on Cube Root of 135

What is the Cube Root of 135?

The cube root of 135 is the number which when multiplied by itself three times gives the product as 135. Since 135 can be expressed as 3 × 3 × 3 × 5. Therefore, the cube root of 135 = ∛(3 × 3 × 3 × 5) = 5.1299.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 135?

Cube Root of 135 by Halley's Method

Its formula is ∛a ≈ x ((x³ + 2a)/(2x³ + a))
where,
a = number whose cube root is being calculated
x = integer guess of its cube root.

Here a = 135
Let us assume x as 5
[∵ 5³ = 125 and 125 is the nearest perfect cube that is less than 135]
⇒ x = 5
Therefore,
∛135 = 5 (5³ + 2 × 135)/(2 × 5³ + 135)) = 5.13
⇒ ∛135 ≈ 5.13
Therefore, the cube root of 135 is 5.13 approximately.

Is the Cube Root of 135 Irrational?

Yes, because ∛135 = ∛(3 × 3 × 3 × 5) = 3 ∛5 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 135 is an irrational number.

☛ Also Check:

Cube Root of 135 Solved Examples

Example 1: The volume of a spherical ball is 135π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 135π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 135
⇒ R = ∛(3/4 × 135) = ∛(3/4) × ∛135 = 0.90856 × 5.12993 (∵ ∛(3/4) = 0.90856 and ∛135 = 5.12993)
⇒ R = 4.66085 in³
Example 2: Given the volume of a cube is 135 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 135 in³ = a³
⇒ a³ = 135
Cube rooting on both sides,
⇒ a = ∛135 in
Since the cube root of 135 is 5.13, therefore, the length of the side of the cube is 5.13 in.
Example 3: What is the value of ∛135 + ∛(-135)?

Solution:

The cube root of -135 is equal to the negative of the cube root of 135.
i.e. ∛-135 = -∛135

Therefore, ∛135 + ∛(-135) = ∛135 - ∛135 = 0

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Cube Root of 135

What is the Value of the Cube Root of 135?

We can express 135 as 3 × 3 × 3 × 5 i.e. ∛135 = ∛(3 × 3 × 3 × 5) = 5.12993. Therefore, the value of the cube root of 135 is 5.12993.

If the Cube Root of 135 is 5.13, Find the Value of ∛0.135.

Let us represent ∛0.135 in p/q form i.e. ∛(135/1000) = 5.13/10 = 0.51. Hence, the value of ∛0.135 = 0.51.

What is the Value of 8 Plus 10 Cube Root 135?

The value of ∛135 is 5.13. So, 8 + 10 × ∛135 = 8 + 10 × 5.13 = 59.3. Hence, the value of 8 plus 10 cube root 135 is 59.3.

What is the Cube of the Cube Root of 135?

The cube of the cube root of 135 is the number 135 itself i.e. (∛135)³ = (135^1/3)³ = 135.

What is the Cube Root of -135?

The cube root of -135 is equal to the negative of the cube root of 135. Therefore, ∛-135 = -(∛135) = -(5.13) = -5.13.

How to Simplify the Cube Root of 135/27?

We know that the cube root of 135 is 5.12993 and the cube root of 27 is 3. Therefore, ∛(135/27) = (∛135)/(∛27) = 5.13/3 = 1.71.