Question

Solve This for Me :-

³√8000​

Answer 1

Step-by-step explanation:

$\sqrt[3]{8000} = 20$

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Answer 2

The value of the cube root of 8000 is 20. It is the real solution of the equation x3 = 8000. The cube root of 8000 is expressed as ∛8000 in radical form and as (8000)⅓ or (8000)0.33 in the exponent form. As the cube root of 8000 is a whole number, 8000 is a perfect cube.

Cube root of 8000: 20Cube root of 8000 in exponential form: (8000)⅓Cube root of 8000 in radical form: ∛8000

What is the Cube Root of 8000?

The cube root of 8000 is the number which when multiplied by itself three times gives the product as 8000. Since 8000 can be expressed as 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5. Therefore, the cube root of 8000 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5) = 20.

How to Calculate the Value of the Cube Root of 8000?

Cube Root of 8000 by Prime FactorizationPrime factorization of 8000 is 2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5Simplifying the above expression: 26 × 53Simplifying further: 203

Therefore, the cube root of 8000 by prime factorization is (2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5)1/3 = 20.

Is the Cube Root of 8000 Irrational?

No, because ∛8000 = ∛(2 × 2 × 2 × 2 × 2 × 2 × 5 × 5 × 5) can be expressed in the form of p/q i.e. 20/1. Therefore, the value of the cube root of 8000 is an integer (rational).