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

Cube Root of 270

The value of the cube root of 270 rounded to 5 decimal places is 6.4633. It is the real solution of the equation x³ = 270. The cube root of 270 is expressed as ∛270 or 3 ∛10 in the radical form and as (270)^⅓ or (270)^0.33 in the exponent form. The prime factorization of 270 is 2 × 3 × 3 × 3 × 5, hence, the cube root of 270 in its lowest radical form is expressed as 3 ∛10.

Cube root of 270: 6.46330407
Cube root of 270 in Exponential Form: (270)^⅓
Cube root of 270 in Radical Form: ∛270 or 3 ∛10

Cube Root of 270

1.	What is the Cube Root of 270?
2.	How to Calculate the Cube Root of 270?
3.	Is the Cube Root of 270 Irrational?
4.	FAQs on Cube Root of 270

What is the Cube Root of 270?

The cube root of 270 is the number which when multiplied by itself three times gives the product as 270. Since 270 can be expressed as 2 × 3 × 3 × 3 × 5. Therefore, the cube root of 270 = ∛(2 × 3 × 3 × 3 × 5) = 6.4633.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 270?

Cube Root of 270 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 = 270
Let us assume x as 6
[∵ 6³ = 216 and 216 is the nearest perfect cube that is less than 270]
⇒ x = 6
Therefore,
∛270 = 6 (6³ + 2 × 270)/(2 × 6³ + 270)) = 6.46
⇒ ∛270 ≈ 6.46
Therefore, the cube root of 270 is 6.46 approximately.

Is the Cube Root of 270 Irrational?

Yes, because ∛270 = ∛(2 × 3 × 3 × 3 × 5) = 3 ∛10 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 270 is an irrational number.

☛ Also Check:

Cube Root of 270 Solved Examples

Example 1: What is the value of ∛270 + ∛(-270)?

Solution:

The cube root of -270 is equal to the negative of the cube root of 270.
i.e. ∛-270 = -∛270

Therefore, ∛270 + ∛(-270) = ∛270 - ∛270 = 0
Example 2: The volume of a spherical ball is 270π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 270π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 270
⇒ R = ∛(3/4 × 270) = ∛(3/4) × ∛270 = 0.90856 × 6.4633 (∵ ∛(3/4) = 0.90856 and ∛270 = 6.4633)
⇒ R = 5.8723 in³
Example 3: Find the real root of the equation x³ − 270 = 0.

Solution:

x³ − 270 = 0 i.e. x³ = 270
Solving for x gives us,
x = ∛270, x = ∛270 × (-1 + √3i))/2 and x = ∛270 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛270
Therefore, the real root of the equation x³ − 270 = 0 is for x = ∛270 = 6.4633.

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 270

What is the Value of the Cube Root of 270?

We can express 270 as 2 × 3 × 3 × 3 × 5 i.e. ∛270 = ∛(2 × 3 × 3 × 3 × 5) = 6.4633. Therefore, the value of the cube root of 270 is 6.4633.

If the Cube Root of 270 is 6.46, Find the Value of ∛0.27.

Let us represent ∛0.27 in p/q form i.e. ∛(270/1000) = 6.46/10 = 0.65. Hence, the value of ∛0.27 = 0.65.

What is the Cube Root of -270?

The cube root of -270 is equal to the negative of the cube root of 270. Therefore, ∛-270 = -(∛270) = -(6.463) = -6.463.

How to Simplify the Cube Root of 270/216?

We know that the cube root of 270 is 6.4633 and the cube root of 216 is 6. Therefore, ∛(270/216) = (∛270)/(∛216) = 6.463/6 = 1.0772.

Is 270 a Perfect Cube?

The number 270 on prime factorization gives 2 × 3 × 3 × 3 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 270 is irrational, hence 270 is not a perfect cube.

Why is the Value of the Cube Root of 270 Irrational?

The value of the cube root of 270 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛270 is irrational.

Math worksheets and
visual curriculum