What is the irrational cube root 81−−√3 rewritten as a product of an integer and another irrational cube root?

Note: You will find the option to add a cubic root symbol in the Algebra ( ×
) keyboard.

1 answer

To rewrite the irrational cube root as a product of an integer and another irrational cube root, we need to find a perfect cube that can be factored out of 81.

81 can be expressed as (3^4) since 3^4 = 81.

81^(1/3) can be written as (3^4)^(1/3).

Using the property of exponents, we can rewrite it as:

(3^4)^(1/3) = 3^(4/3).

Therefore, the irrational cube root 81^(1/3) can be written as the product 3 * (3^(1/3)).