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Cube Root of 90

The value of the cube root of 90 rounded to 4 decimal places is 4.4814. It is the real solution of the equation x³ = 90. The cube root of 90 is expressed as ∛90 in the radical form and as (90)^⅓ or (90)^0.33 in the exponent form. The prime factorization of 90 is 2 × 3 × 3 × 5, hence, the cube root of 90 in its lowest radical form is expressed as ∛90.

Cube root of 90: 4.481404747
Cube root of 90 in Exponential Form: (90)^⅓
Cube root of 90 in Radical Form: ∛90

Cube Root of 90

1.	What is the Cube Root of 90?
2.	How to Calculate the Cube Root of 90?
3.	Is the Cube Root of 90 Irrational?
4.	FAQs on Cube Root of 90

What is the Cube Root of 90?

The cube root of 90 is the number which when multiplied by itself three times gives the product as 90. Since 90 can be expressed as 2 × 3 × 3 × 5. Therefore, the cube root of 90 = ∛(2 × 3 × 3 × 5) = 4.4814.

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How to Calculate the Value of the Cube Root of 90?

Cube Root of 90 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 = 90
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 90]
⇒ x = 4
Therefore,
∛90 = 4 (4³ + 2 × 90)/(2 × 4³ + 90)) = 4.48
⇒ ∛90 ≈ 4.48
Therefore, the cube root of 90 is 4.48 approximately.

Is the Cube Root of 90 Irrational?

Yes, because ∛90 = ∛(2 × 3 × 3 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 90 is an irrational number.

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Cube Root of 90 Solved Examples

Example 1: Find the real root of the equation x³ − 90 = 0.

Solution:

x³ − 90 = 0 i.e. x³ = 90
Solving for x gives us,
x = ∛90, x = ∛90 × (-1 + √3i))/2 and x = ∛90 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛90
Therefore, the real root of the equation x³ − 90 = 0 is for x = ∛90 = 4.4814.
Example 2: The volume of a spherical ball is 90π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 90π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 90
⇒ R = ∛(3/4 × 90) = ∛(3/4) × ∛90 = 0.90856 × 4.4814 (∵ ∛(3/4) = 0.90856 and ∛90 = 4.4814)
⇒ R = 4.07162 in³
Example 3: Given the volume of a cube is 90 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 90 in³ = a³
⇒ a³ = 90
Cube rooting on both sides,
⇒ a = ∛90 in
Since the cube root of 90 is 4.48, therefore, the length of the side of the cube is 4.48 in.

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FAQs on Cube Root of 90

What is the Value of the Cube Root of 90?

We can express 90 as 2 × 3 × 3 × 5 i.e. ∛90 = ∛(2 × 3 × 3 × 5) = 4.4814. Therefore, the value of the cube root of 90 is 4.4814.

What is the Value of 3 Plus 2 Cube Root 90?

The value of ∛90 is 4.481. So, 3 + 2 × ∛90 = 3 + 2 × 4.481 = 11.962. Hence, the value of 3 plus 2 cube root 90 is 11.962.

What is the Cube Root of -90?

The cube root of -90 is equal to the negative of the cube root of 90. Therefore, ∛-90 = -(∛90) = -(4.481) = -4.481.

Why is the Value of the Cube Root of 90 Irrational?

The value of the cube root of 90 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛90 is irrational.

How to Simplify the Cube Root of 90/729?

We know that the cube root of 90 is 4.4814 and the cube root of 729 is 9. Therefore, ∛(90/729) = (∛90)/(∛729) = 4.481/9 = 0.4979.

What is the Cube of the Cube Root of 90?

The cube of the cube root of 90 is the number 90 itself i.e. (∛90)³ = (90^1/3)³ = 90.

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