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

Cube Root of 5

The value of the cube root of 5 rounded to 6 decimal places is 1.709976. It is the real solution of the equation x³ = 5. The cube root of 5 is expressed as ∛5 in the radical form and as (5)^⅓ or (5)^0.33 in the exponent form. The prime factorization of 5 is 5, hence, the cube root of 5 in its lowest radical form is expressed as ∛5.

Cube root of 5: 1.709975947
Cube root of 5 in Exponential Form: (5)^⅓
Cube root of 5 in Radical Form: ∛5

Cube Root of 5

1.	What is the Cube Root of 5?
2.	How to Calculate the Cube Root of 5?
3.	Is the Cube Root of 5 Irrational?
4.	FAQs on Cube Root of 5

What is the Cube Root of 5?

The cube root of 5 is the number which when multiplied by itself three times gives the product as 5. The number 5 is prime. Therefore, the cube root of 5 = ∛5 = 1.71.

☛ Check: Cube Root Calculator

How to Calculate the Value of the Cube Root of 5?

Cube Root of 5 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 = 5
Let us assume x as 1
[∵ 1³ = 1 and 1 is the nearest perfect cube that is less than 5]
⇒ x = 1
Therefore,
∛5 = 1 (1³ + 2 × 5)/(2 × 1³ + 5)) = 1.57
⇒ ∛5 ≈ 1.57
Therefore, the cube root of 5 is 1.57 approximately.

Is the Cube Root of 5 Irrational?

Yes, because ∛5 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the value of the cube root of 5 is an irrational number.

☛ Also Check:

Cube Root of 5 Solved Examples

Example 1: Find the real root of the equation x³ − 5 = 0.

Solution:

x³ − 5 = 0 i.e. x³ = 5
Solving for x gives us,
x = ∛5, x = ∛5 × (-1 + √3i))/2 and x = ∛5 × (-1 - √3i))/2
where i is called the imaginary unit and is equal to √-1.
Ignoring imaginary roots,
x = ∛5
Therefore, the real root of the equation x³ − 5 = 0 is for x = ∛5 = 1.71.
Example 2: Given the volume of a cube is 5 in³. Find the length of the side of the cube.

Solution:

Volume of the Cube = 5 in³ = a³
⇒ a³ = 5
Cube rooting on both sides,
⇒ a = ∛5 in
Since the cube root of 5 is 1.71, therefore, the length of the side of the cube is 1.71 in.
Example 3: What is the value of ∛5 ÷ ∛(-5)?

Solution:

The cube root of -5 is equal to the negative of the cube root of 5.
⇒ ∛-5 = -∛5

Therefore,
⇒ ∛5/∛(-5) = ∛5/(-∛5) = -1

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 5

What is the Value of the Cube Root of 5?

The value of the cube root of 5 is 1.70998.

Why is the Value of the Cube Root of 5 Irrational?

The value of the cube root of 5 cannot be expressed in the form of p/q where q ≠ 0. Therefore, the number ∛5 is irrational.

What is the Cube of the Cube Root of 5?

The cube of the cube root of 5 is the number 5 itself i.e. (∛5)³ = (5^1/3)³ = 5.

Is 5 a Perfect Cube?

The number 5 is prime. Here, the prime factor 5 is not in the power of 3 and this implies that the cube root of 5 is irrational, hence 5 is not a perfect cube.

What is the Cube Root of -5?

The cube root of -5 is equal to the negative of the cube root of 5. Therefore, ∛-5 = -(∛5) = -(1.71) = -1.71.

What is the Value of 1 Plus 7 Cube Root 5?

The value of ∛5 is 1.71. So, 1 + 7 × ∛5 = 1 + 7 × 1.71 = 12.969999999999999. Hence, the value of 1 plus 7 cube root 5 is 12.969999999999999.

Math worksheets and
visual curriculum