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Cube Root of 10

The value of the cube root of 10 rounded to 4 decimal places is 2.1544. It is the real solution of the equation x³ = 10. The cube root of 10 is expressed as ∛10 in the radical form and as (10)^⅓ or (10)^0.33 in the exponent form. The prime factorization of 10 is 2 × 5, hence, the cube root of 10 in its lowest radical form is expressed as ∛10.

Cube root of 10: 2.15443469
Cube root of 10 in Exponential Form: (10)^⅓
Cube root of 10 in Radical Form: ∛10

1.	What is the Cube Root of 10?
2.	How to Calculate the Cube Root of 10?
3.	Is the Cube Root of 10 Irrational?
4.	FAQs on Cube Root of 10

What is the Cube Root of 10?

The cube root of 10 is the number which when multiplied by itself three times gives the product as 10. Since 10 can be expressed as 2 × 5. Therefore, the cube root of 10 = ∛(2 × 5) = 2.1544.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 10?

Cube Root of 10 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 = 10
Let us assume x as 2
[∵ 2³ = 8 and 8 is the nearest perfect cube that is less than 10]
⇒ x = 2
Therefore,
∛10 = 2 (2³ + 2 × 10)/(2 × 2³ + 10)) = 2.15
⇒ ∛10 ≈ 2.15
Therefore, the cube root of 10 is 2.15 approximately.

Is the Cube Root of 10 Irrational?

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

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Cube Root of 10 Solved Examples

Example 1: The volume of a spherical ball is 10π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 10π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 10
⇒ R = ∛(3/4 × 10) = ∛(3/4) × ∛10 = 0.90856 × 2.15443 (∵ ∛(3/4) = 0.90856 and ∛10 = 2.15443)
⇒ R = 1.95743 in³
Example 2: Given the volume of a cube is 10 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 10 in³ = a³
⇒ a³ = 10
Cube rooting on both sides,
⇒ a = ∛10 in
Since the cube root of 10 is 2.15, therefore, the length of the side of the cube is 2.15 in.
Example 3: What is the value of ∛10 ÷ ∛(-10)?

Solution:

The cube root of -10 is equal to the negative of the cube root of 10.
⇒ ∛-10 = -∛10

Therefore,
⇒ ∛10/∛(-10) = ∛10/(-∛10) = -1

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FAQs on Cube Root of 10

What is the Value of the Cube Root of 10?

We can express 10 as 2 × 5 i.e. ∛10 = ∛(2 × 5) = 2.15443. Therefore, the value of the cube root of 10 is 2.15443.

Why is the Value of the Cube Root of 10 Irrational?

The value of the cube root of 10 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛10 is irrational.

What is the Cube of the Cube Root of 10?

The cube of the cube root of 10 is the number 10 itself i.e. (∛10)³ = (10^1/3)³ = 10.

If the Cube Root of 10 is 2.15, Find the Value of ∛0.01.

Let us represent ∛0.01 in p/q form i.e. ∛(10/1000) = 2.15/10 = 0.22. Hence, the value of ∛0.01 = 0.22.

Is 10 a Perfect Cube?

The number 10 on prime factorization gives 2 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 10 is irrational, hence 10 is not a perfect cube.

What is the Value of 4 Plus 1 Cube Root 10?

The value of ∛10 is 2.154. So, 4 + 1 × ∛10 = 4 + 1 × 2.154 = 6.154. Hence, the value of 4 plus 1 cube root 10 is 6.154.