A day full of math games & activities. Find one near you.

Cube Root of 675

The value of the cube root of 675 rounded to 7 decimal places is 8.7720532. It is the real solution of the equation x³ = 675. The cube root of 675 is expressed as ∛675 or 3 ∛25 in the radical form and as (675)^⅓ or (675)^0.33 in the exponent form. The prime factorization of 675 is 3 × 3 × 3 × 5 × 5, hence, the cube root of 675 in its lowest radical form is expressed as 3 ∛25.

Cube root of 675: 8.772053215
Cube root of 675 in Exponential Form: (675)^⅓
Cube root of 675 in Radical Form: ∛675 or 3 ∛25

Cube Root of 675

1.	What is the Cube Root of 675?
2.	How to Calculate the Cube Root of 675?
3.	Is the Cube Root of 675 Irrational?
4.	FAQs on Cube Root of 675

What is the Cube Root of 675?

The cube root of 675 is the number which when multiplied by itself three times gives the product as 675. Since 675 can be expressed as 3 × 3 × 3 × 5 × 5. Therefore, the cube root of 675 = ∛(3 × 3 × 3 × 5 × 5) = 8.7721.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 675?

Cube Root of 675 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 = 675
Let us assume x as 8
[∵ 8³ = 512 and 512 is the nearest perfect cube that is less than 675]
⇒ x = 8
Therefore,
∛675 = 8 (8³ + 2 × 675)/(2 × 8³ + 675)) = 8.77
⇒ ∛675 ≈ 8.77
Therefore, the cube root of 675 is 8.77 approximately.

Is the Cube Root of 675 Irrational?

Yes, because ∛675 = ∛(3 × 3 × 3 × 5 × 5) = 3 ∛25 and it cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 675 is an irrational number.

☛ Also Check:

Cube Root of 675 Solved Examples

Example 1: Find the real root of the equation x³ − 675 = 0.

Solution:

x³ − 675 = 0 i.e. x³ = 675
Solving for x gives us,
x = ∛675, x = ∛675 × (-1 + √3i))/2 and x = ∛675 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛675
Therefore, the real root of the equation x³ − 675 = 0 is for x = ∛675 = 8.7721.
Example 2: The volume of a spherical ball is 675π in³. What is the radius of this ball?

Solution:

Volume of the spherical ball = 675π in³
= 4/3 × π × R³
⇒ R³ = 3/4 × 675
⇒ R = ∛(3/4 × 675) = ∛(3/4) × ∛675 = 0.90856 × 8.77205 (∵ ∛(3/4) = 0.90856 and ∛675 = 8.77205)
⇒ R = 7.96993 in³
Example 3: Given the volume of a cube is 675 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 675 in³ = a³
⇒ a³ = 675
Cube rooting on both sides,
⇒ a = ∛675 in
Since the cube root of 675 is 8.77, therefore, the length of the side of the cube is 8.77 in.

go to slide go to slide go to slide

Ready to see the world through math’s eyes?

Math is at the core of everything we do. Enjoy solving real-world math problems in live classes and become an expert at everything.

Book a Free Trial Class

FAQs on Cube Root of 675

What is the Value of the Cube Root of 675?

We can express 675 as 3 × 3 × 3 × 5 × 5 i.e. ∛675 = ∛(3 × 3 × 3 × 5 × 5) = 8.77205. Therefore, the value of the cube root of 675 is 8.77205.

What is the Cube of the Cube Root of 675?

The cube of the cube root of 675 is the number 675 itself i.e. (∛675)³ = (675^1/3)³ = 675.

What is the Value of 20 Plus 4 Cube Root 675?

The value of ∛675 is 8.772. So, 20 + 4 × ∛675 = 20 + 4 × 8.772 = 55.088. Hence, the value of 20 plus 4 cube root 675 is 55.088.

How to Simplify the Cube Root of 675/125?

We know that the cube root of 675 is 8.77205 and the cube root of 125 is 5. Therefore, ∛(675/125) = (∛675)/(∛125) = 8.772/5 = 1.7544.

Why is the Value of the Cube Root of 675 Irrational?

The value of the cube root of 675 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛675 is irrational.

What is the Cube Root of -675?

The cube root of -675 is equal to the negative of the cube root of 675. Therefore, ∛-675 = -(∛675) = -(8.772) = -8.772.

Math worksheets and
visual curriculum