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Cube Root of 750

The value of the cube root of 750 rounded to 5 decimal places is 9.0856. It is the real solution of the equation x³ = 750. The cube root of 750 is expressed as ∛750 or 5 ∛6 in the radical form and as (750)^⅓ or (750)^0.33 in the exponent form. The prime factorization of 750 is 2 × 3 × 5 × 5 × 5, hence, the cube root of 750 in its lowest radical form is expressed as 5 ∛6.

Cube root of 750: 9.085602964
Cube root of 750 in Exponential Form: (750)^⅓
Cube root of 750 in Radical Form: ∛750 or 5 ∛6

Cube Root of 750

1.	What is the Cube Root of 750?
2.	How to Calculate the Cube Root of 750?
3.	Is the Cube Root of 750 Irrational?
4.	FAQs on Cube Root of 750

What is the Cube Root of 750?

The cube root of 750 is the number which when multiplied by itself three times gives the product as 750. Since 750 can be expressed as 2 × 3 × 5 × 5 × 5. Therefore, the cube root of 750 = ∛(2 × 3 × 5 × 5 × 5) = 9.0856.

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How to Calculate the Value of the Cube Root of 750?

Cube Root of 750 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 = 750
Let us assume x as 9
[∵ 9³ = 729 and 729 is the nearest perfect cube that is less than 750]
⇒ x = 9
Therefore,
∛750 = 9 (9³ + 2 × 750)/(2 × 9³ + 750)) = 9.09
⇒ ∛750 ≈ 9.09
Therefore, the cube root of 750 is 9.09 approximately.

Is the Cube Root of 750 Irrational?

Yes, because ∛750 = ∛(2 × 3 × 5 × 5 × 5) = 5 ∛6 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 750 is an irrational number.

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Cube Root of 750 Solved Examples

Example 1: What is the value of ∛750 ÷ ∛(-750)?

Solution:

The cube root of -750 is equal to the negative of the cube root of 750.
⇒ ∛-750 = -∛750

Therefore,
⇒ ∛750/∛(-750) = ∛750/(-∛750) = -1
Example 2: Find the real root of the equation x³ − 750 = 0.

Solution:

x³ − 750 = 0 i.e. x³ = 750
Solving for x gives us,
x = ∛750, x = ∛750 × (-1 + √3i))/2 and x = ∛750 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛750
Therefore, the real root of the equation x³ − 750 = 0 is for x = ∛750 = 9.0856.
Example 3: The volume of a spherical ball is 750π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 750π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 750
⇒ R = ∛(3/4 × 750) = ∛(3/4) × ∛750 = 0.90856 × 9.0856 (∵ ∛(3/4) = 0.90856 and ∛750 = 9.0856)
⇒ R = 8.25481 in³

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FAQs on Cube Root of 750

What is the Value of the Cube Root of 750?

We can express 750 as 2 × 3 × 5 × 5 × 5 i.e. ∛750 = ∛(2 × 3 × 5 × 5 × 5) = 9.0856. Therefore, the value of the cube root of 750 is 9.0856.

Why is the Value of the Cube Root of 750 Irrational?

The value of the cube root of 750 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛750 is irrational.

If the Cube Root of 750 is 9.09, Find the Value of ∛0.75.

Let us represent ∛0.75 in p/q form i.e. ∛(750/1000) = 9.09/10 = 0.91. Hence, the value of ∛0.75 = 0.91.

Is 750 a Perfect Cube?

The number 750 on prime factorization gives 2 × 3 × 5 × 5 × 5. Here, the prime factor 2 is not in the power of 3. Therefore the cube root of 750 is irrational, hence 750 is not a perfect cube.

What is the Cube of the Cube Root of 750?

The cube of the cube root of 750 is the number 750 itself i.e. (∛750)³ = (750^1/3)³ = 750.

How to Simplify the Cube Root of 750/216?

We know that the cube root of 750 is 9.0856 and the cube root of 216 is 6. Therefore, ∛(750/216) = (∛750)/(∛216) = 9.086/6 = 1.5143.

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