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Cube Root of 72

The value of the cube root of 72 rounded to 5 decimal places is 4.16017. It is the real solution of the equation x³ = 72. The cube root of 72 is expressed as ∛72 or 2 ∛9 in the radical form and as (72)^⅓ or (72)^0.33 in the exponent form. The prime factorization of 72 is 2 × 2 × 2 × 3 × 3, hence, the cube root of 72 in its lowest radical form is expressed as 2 ∛9.

Cube root of 72: 4.160167646
Cube root of 72 in Exponential Form: (72)^⅓
Cube root of 72 in Radical Form: ∛72 or 2 ∛9

Cube Root of 72

1.	What is the Cube Root of 72?
2.	How to Calculate the Cube Root of 72?
3.	Is the Cube Root of 72 Irrational?
4.	FAQs on Cube Root of 72

What is the Cube Root of 72?

The cube root of 72 is the number which when multiplied by itself three times gives the product as 72. Since 72 can be expressed as 2 × 2 × 2 × 3 × 3. Therefore, the cube root of 72 = ∛(2 × 2 × 2 × 3 × 3) = 4.1602.

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How to Calculate the Value of the Cube Root of 72?

Cube Root of 72 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 = 72
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 72]
⇒ x = 4
Therefore,
∛72 = 4 (4³ + 2 × 72)/(2 × 4³ + 72)) = 4.16
⇒ ∛72 ≈ 4.16
Therefore, the cube root of 72 is 4.16 approximately.

Is the Cube Root of 72 Irrational?

Yes, because ∛72 = ∛(2 × 2 × 2 × 3 × 3) = 2 ∛9 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 72 is an irrational number.

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Cube Root of 72 Solved Examples

Example 1: The volume of a spherical ball is 72π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 72π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 72
⇒ R = ∛(3/4 × 72) = ∛(3/4) × ∛72 = 0.90856 × 4.16017 (∵ ∛(3/4) = 0.90856 and ∛72 = 4.16017)
⇒ R = 3.77976 in³
Example 2: Find the real root of the equation x³ − 72 = 0.

Solution:

x³ − 72 = 0 i.e. x³ = 72
Solving for x gives us,
x = ∛72, x = ∛72 × (-1 + √3i))/2 and x = ∛72 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛72
Therefore, the real root of the equation x³ − 72 = 0 is for x = ∛72 = 4.1602.
Example 3: What is the value of ∛72 ÷ ∛(-72)?

Solution:

The cube root of -72 is equal to the negative of the cube root of 72.
⇒ ∛-72 = -∛72

Therefore,
⇒ ∛72/∛(-72) = ∛72/(-∛72) = -1

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FAQs on Cube Root of 72

What is the Value of the Cube Root of 72?

We can express 72 as 2 × 2 × 2 × 3 × 3 i.e. ∛72 = ∛(2 × 2 × 2 × 3 × 3) = 4.16017. Therefore, the value of the cube root of 72 is 4.16017.

Is 72 a Perfect Cube?

The number 72 on prime factorization gives 2 × 2 × 2 × 3 × 3. Here, the prime factor 3 is not in the power of 3. Therefore the cube root of 72 is irrational, hence 72 is not a perfect cube.

How to Simplify the Cube Root of 72/216?

We know that the cube root of 72 is 4.16017 and the cube root of 216 is 6. Therefore, ∛(72/216) = (∛72)/(∛216) = 4.16/6 = 0.6933.

If the Cube Root of 72 is 4.16, Find the Value of ∛0.072.

Let us represent ∛0.072 in p/q form i.e. ∛(72/1000) = 4.16/10 = 0.42. Hence, the value of ∛0.072 = 0.42.

What is the Cube Root of -72?

The cube root of -72 is equal to the negative of the cube root of 72. Therefore, ∛-72 = -(∛72) = -(4.16) = -4.16.

What is the Value of 4 Plus 19 Cube Root 72?

The value of ∛72 is 4.16. So, 4 + 19 × ∛72 = 4 + 19 × 4.16 = 83.04. Hence, the value of 4 plus 19 cube root 72 is 83.04.

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