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Cube Root of 900

The value of the cube root of 900 rounded to 5 decimal places is 9.65489. It is the real solution of the equation x³ = 900. The cube root of 900 is expressed as ∛900 in the radical form and as (900)^⅓ or (900)^0.33 in the exponent form. The prime factorization of 900 is 2 × 2 × 3 × 3 × 5 × 5, hence, the cube root of 900 in its lowest radical form is expressed as ∛900.

Cube root of 900: 9.654893846
Cube root of 900 in Exponential Form: (900)^⅓
Cube root of 900 in Radical Form: ∛900

Cube Root of 900

1.	What is the Cube Root of 900?
2.	How to Calculate the Cube Root of 900?
3.	Is the Cube Root of 900 Irrational?
4.	FAQs on Cube Root of 900

What is the Cube Root of 900?

The cube root of 900 is the number which when multiplied by itself three times gives the product as 900. Since 900 can be expressed as 2 × 2 × 3 × 3 × 5 × 5. Therefore, the cube root of 900 = ∛(2 × 2 × 3 × 3 × 5 × 5) = 9.6549.

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How to Calculate the Value of the Cube Root of 900?

Cube Root of 900 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 = 900
Let us assume x as 9
[∵ 9³ = 729 and 729 is the nearest perfect cube that is less than 900]
⇒ x = 9
Therefore,
∛900 = 9 (9³ + 2 × 900)/(2 × 9³ + 900)) = 9.65
⇒ ∛900 ≈ 9.65
Therefore, the cube root of 900 is 9.65 approximately.

Is the Cube Root of 900 Irrational?

Yes, because ∛900 = ∛(2 × 2 × 3 × 3 × 5 × 5) and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 900 is an irrational number.

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Cube Root of 900 Solved Examples

Example 1: Find the real root of the equation x³ − 900 = 0.

Solution:

x³ − 900 = 0 i.e. x³ = 900
Solving for x gives us,
x = ∛900, x = ∛900 × (-1 + √3i))/2 and x = ∛900 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛900
Therefore, the real root of the equation x³ − 900 = 0 is for x = ∛900 = 9.6549.
Example 2: The volume of a spherical ball is 900π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 900π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 900
⇒ R = ∛(3/4 × 900) = ∛(3/4) × ∛900 = 0.90856 × 9.65489 (∵ ∛(3/4) = 0.90856 and ∛900 = 9.65489)
⇒ R = 8.77205 in³
Example 3: Given the volume of a cube is 900 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 900 in³ = a³
⇒ a³ = 900
Cube rooting on both sides,
⇒ a = ∛900 in
Since the cube root of 900 is 9.65, therefore, the length of the side of the cube is 9.65 in.

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FAQs on Cube Root of 900

What is the Value of the Cube Root of 900?

We can express 900 as 2 × 2 × 3 × 3 × 5 × 5 i.e. ∛900 = ∛(2 × 2 × 3 × 3 × 5 × 5) = 9.65489. Therefore, the value of the cube root of 900 is 9.65489.

What is the Value of 13 Plus 4 Cube Root 900?

The value of ∛900 is 9.655. So, 13 + 4 × ∛900 = 13 + 4 × 9.655 = 51.62. Hence, the value of 13 plus 4 cube root 900 is 51.62.

How to Simplify the Cube Root of 900/729?

We know that the cube root of 900 is 9.65489 and the cube root of 729 is 9. Therefore, ∛(900/729) = (∛900)/(∛729) = 9.655/9 = 1.0728.

Is 900 a Perfect Cube?

The number 900 on prime factorization gives 2 × 2 × 3 × 3 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 900 is irrational, hence 900 is not a perfect cube.

What is the Cube Root of -900?

The cube root of -900 is equal to the negative of the cube root of 900. Therefore, ∛-900 = -(∛900) = -(9.655) = -9.655.

Why is the Value of the Cube Root of 900 Irrational?

The value of the cube root of 900 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛900 is irrational.

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