The Cube Root Of 8

Cube Root of 8

The value of the cube root of eight is 2. It is the real solution of the equation 10^three = 8. The cube root of 8 is expressed as ∛8 in radical form and as (8)^⅓ or (viii)^0.33 in the exponent grade. As the cube root of 8 is a whole number, 8 is a perfect cube.

• Cube root of eight: 2
• Cube root of eight in exponential form: (8)^⅓
• Cube root of 8 in radical form: ∛8

1.	What is the Cube Root of 8?
2.	How to Calculate the Cube Root of eight?
3.	Is the Cube Root of 8 Irrational?
4.	FAQs on Cube Root of viii

What is the Cube Root of 8?

The cube root of eight is the number which when multiplied by itself 3 times gives the production as eight. Since 8 can be expressed as two × ii × ii. Therefore, the cube root of 8 = ∛(2 × 2 × 2) = two.

How to Calculate the Value of the Cube Root of 8?

Cube Root of viii past Prime Factorization

• Prime factorization of viii is 2 × two × 2
• Simplifying the above expression: two^three

Therefore, the cube root of 8 by prime factorization is (2 × 2 × ii)^1/3 = 2.

Is the Cube Root of eight Irrational?

No, considering ∛8 = ∛(2 × ii × 2) can exist expressed in the form of p/q i.e. ii/1. Therefore, the value of the cube root of 8 is an integer (rational).

☛ Also Bank check:

• Cube Root of 96
• Cube Root of 864
• Cube Root of 529
• Cube Root of 91
• Cube Root of 22
• Cube Root of lxx
• Cube Root of 2000

Cube Root of 8 Solved Examples

1. Example 1: Find the real root of the equation x³ − 8 = 0.

   Solution:

   x³ − 8 = 0 i.east. 10³ = 8
   Solving for ten gives u.s.a.,
   10 = ∛8, x = ∛8 × (-ane + √3i))/2 and ten = ∛8 × (-1 - √3i))/2
   where i is chosen the imaginary unit and is equal to √-1.
   Ignoring imaginary roots,
   x = ∛8
   Therefore, the real root of the equation 10³ − 8 = 0 is for x = ∛viii = 2.

2. Instance 2: What is the value of ∛viii + ∛(-8)?

   Solution:

   The cube root of -eight is equal to the negative of the cube root of 8.
   i.due east. ∛-8 = -∛eight

   Therefore, ∛8 + ∛(-eight) = ∛8 - ∛8 = 0

3. Case iii: The book of a spherical ball is 8π in³. What is the radius of this ball?

   Solution:

   Book of the spherical ball = 8π inⁱⁱⁱ
   = 4/three × π × R³
   ⇒ Rⁱⁱⁱ = 3/4 × eight
   ⇒ R = ∛(iii/4 × 8) = ∛(3/4) × ∛viii = 0.90856 × two (∵ ∛(3/4) = 0.90856 and ∛viii = two)
   ⇒ R = 1.81712 inⁱⁱⁱ

go to slidego to slidego 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 proficient at everything.

Volume a Free Trial Class

FAQs on Cube Root of eight

What is the Value of the Cube Root of 8?

Nosotros can express 8 as two × 2 × ii i.eastward. ∛8 = ∛(ii × 2 × 2) = 2. Therefore, the value of the cube root of 8 is ii.

What is the Cube Root of -8?

The cube root of -8 is equal to the negative of the cube root of 8. Therefore, ∛-eight = -(∛eight) = -(2) = -2.

Is 8 a Perfect Cube?

The number viii on prime factorization gives 2 × two × 2. On combining the prime factors in groups of 3 gives two. So, the cube root of 8 = ∛(2 × 2 × ii) = 2 (perfect cube).

How to Simplify the Cube Root of viii/512?

We know that the cube root of viii is 2 and the cube root of 512 is 8. Therefore, ∛(8/512) = (∛eight)/(∛512) = 2/8 = 0.25.

If the Cube Root of 8 is ii, Notice the Value of ∛0.008.

Let united states of america represent ∛0.008 in p/q form i.e. ∛(8/one thousand) = 2/10 = 0.2. Hence, the value of ∛0.008 = 0.2.

Why is the value of the Cube Root of eight Rational?

The value of the cube root of 8 tin exist expressed in the form of p/q i.due east. = 2/1, where q ≠ 0. Therefore, the ∛8 is rational.

The Cube Root Of 8,

Source: https://www.cuemath.com/algebra/cube-root-of-8/

Posted by: gardnerstione.blogspot.com

Share this post