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Cube Root of 88

The value of the cube root of 88 rounded to 6 decimal places is 4.44796. It is the real solution of the equation x³ = 88. The cube root of 88 is expressed as ∛88 or 2 ∛11 in the radical form and as (88)^⅓ or (88)^0.33 in the exponent form. The prime factorization of 88 is 2 × 2 × 2 × 11, hence, the cube root of 88 in its lowest radical form is expressed as 2 ∛11.

Cube root of 88: 4.447960181
Cube root of 88 in Exponential Form: (88)^⅓
Cube root of 88 in Radical Form: ∛88 or 2 ∛11

Cube Root of 88

1.	What is the Cube Root of 88?
2.	How to Calculate the Cube Root of 88?
3.	Is the Cube Root of 88 Irrational?
4.	FAQs on Cube Root of 88

What is the Cube Root of 88?

The cube root of 88 is the number which when multiplied by itself three times gives the product as 88. Since 88 can be expressed as 2 × 2 × 2 × 11. Therefore, the cube root of 88 = ∛(2 × 2 × 2 × 11) = 4.448.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 88?

Cube Root of 88 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 = 88
Let us assume x as 4
[∵ 4³ = 64 and 64 is the nearest perfect cube that is less than 88]
⇒ x = 4
Therefore,
∛88 = 4 (4³ + 2 × 88)/(2 × 4³ + 88)) = 4.44
⇒ ∛88 ≈ 4.44
Therefore, the cube root of 88 is 4.44 approximately.

Is the Cube Root of 88 Irrational?

Yes, because ∛88 = ∛(2 × 2 × 2 × 11) = 2 ∛11 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 88 is an irrational number.

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Cube Root of 88 Solved Examples

Example 1: What is the value of ∛88 ÷ ∛(-88)?

Solution:

The cube root of -88 is equal to the negative of the cube root of 88.
⇒ ∛-88 = -∛88

Therefore,
⇒ ∛88/∛(-88) = ∛88/(-∛88) = -1
Example 2: Find the real root of the equation x³ − 88 = 0.

Solution:

x³ − 88 = 0 i.e. x³ = 88
Solving for x gives us,
x = ∛88, x = ∛88 × (-1 + √3i))/2 and x = ∛88 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛88
Therefore, the real root of the equation x³ − 88 = 0 is for x = ∛88 = 4.448.
Example 3: The volume of a spherical ball is 88π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 88π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 88
⇒ R = ∛(3/4 × 88) = ∛(3/4) × ∛88 = 0.90856 × 4.44796 (∵ ∛(3/4) = 0.90856 and ∛88 = 4.44796)
⇒ R = 4.04124 in³

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FAQs on Cube Root of 88

What is the Value of the Cube Root of 88?

We can express 88 as 2 × 2 × 2 × 11 i.e. ∛88 = ∛(2 × 2 × 2 × 11) = 4.44796. Therefore, the value of the cube root of 88 is 4.44796.

If the Cube Root of 88 is 4.45, Find the Value of ∛0.088.

Let us represent ∛0.088 in p/q form i.e. ∛(88/1000) = 4.45/10 = 0.44. Hence, the value of ∛0.088 = 0.44.

What is the Cube Root of -88?

The cube root of -88 is equal to the negative of the cube root of 88. Therefore, ∛-88 = -(∛88) = -(4.448) = -4.448.

Is 88 a Perfect Cube?

The number 88 on prime factorization gives 2 × 2 × 2 × 11. Here, the prime factor 11 is not in the power of 3. Therefore the cube root of 88 is irrational, hence 88 is not a perfect cube.

How to Simplify the Cube Root of 88/64?

We know that the cube root of 88 is 4.44796 and the cube root of 64 is 4. Therefore, ∛(88/64) = (∛88)/(∛64) = 4.448/4 = 1.112.

Why is the Value of the Cube Root of 88 Irrational?

The value of the cube root of 88 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛88 is irrational.

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