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Cube Root of 70

The value of the cube root of 70 rounded to 5 decimal places is 4.12129. It is the real solution of the equation x³ = 70. The cube root of 70 is expressed as ∛70 in the radical form and as (70)^⅓ or (70)^0.33 in the exponent form. The prime factorization of 70 is 2 × 5 × 7, hence, the cube root of 70 in its lowest radical form is expressed as ∛70.

Cube root of 70: 4.1212853
Cube root of 70 in Exponential Form: (70)^⅓
Cube root of 70 in Radical Form: ∛70

Cube Root of 70

1.	What is the Cube Root of 70?
2.	How to Calculate the Cube Root of 70?
3.	Is the Cube Root of 70 Irrational?
4.	FAQs on Cube Root of 70

What is the Cube Root of 70?

The cube root of 70 is the number which when multiplied by itself three times gives the product as 70. Since 70 can be expressed as 2 × 5 × 7. Therefore, the cube root of 70 = ∛(2 × 5 × 7) = 4.1213.

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How to Calculate the Value of the Cube Root of 70?

Cube Root of 70 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 = 70
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 70]
⇒ x = 4
Therefore,
∛70 = 4 (4³ + 2 × 70)/(2 × 4³ + 70)) = 4.12
⇒ ∛70 ≈ 4.12
Therefore, the cube root of 70 is 4.12 approximately.

Is the Cube Root of 70 Irrational?

Yes, because ∛70 = ∛(2 × 5 × 7) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 70 is an irrational number.

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Cube Root of 70 Solved Examples

Example 1: The volume of a spherical ball is 70π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 70π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 70
⇒ R = ∛(3/4 × 70) = ∛(3/4) × ∛70 = 0.90856 × 4.12129 (∵ ∛(3/4) = 0.90856 and ∛70 = 4.12129)
⇒ R = 3.74444 in³
Example 2: Find the real root of the equation x³ − 70 = 0.

Solution:

x³ − 70 = 0 i.e. x³ = 70
Solving for x gives us,
x = ∛70, x = ∛70 × (-1 + √3i))/2 and x = ∛70 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛70
Therefore, the real root of the equation x³ − 70 = 0 is for x = ∛70 = 4.1213.
Example 3: What is the value of ∛70 + ∛(-70)?

Solution:

The cube root of -70 is equal to the negative of the cube root of 70.
i.e. ∛-70 = -∛70

Therefore, ∛70 + ∛(-70) = ∛70 - ∛70 = 0

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FAQs on Cube Root of 70

What is the Value of the Cube Root of 70?

We can express 70 as 2 × 5 × 7 i.e. ∛70 = ∛(2 × 5 × 7) = 4.12129. Therefore, the value of the cube root of 70 is 4.12129.

Is 70 a Perfect Cube?

The number 70 on prime factorization gives 2 × 5 × 7. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 70 is irrational, hence 70 is not a perfect cube.

What is the Value of 9 Plus 15 Cube Root 70?

The value of ∛70 is 4.121. So, 9 + 15 × ∛70 = 9 + 15 × 4.121 = 70.815. Hence, the value of 9 plus 15 cube root 70 is 70.815.

Why is the Value of the Cube Root of 70 Irrational?

The value of the cube root of 70 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛70 is irrational.

What is the Cube of the Cube Root of 70?

The cube of the cube root of 70 is the number 70 itself i.e. (∛70)³ = (70^1/3)³ = 70.

If the Cube Root of 70 is 4.12, Find the Value of ∛0.07.

Let us represent ∛0.07 in p/q form i.e. ∛(70/1000) = 4.12/10 = 0.41. Hence, the value of ∛0.07 = 0.41.

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