Rewrite the irrational cube root root(189, 3) as the product of an integer and another irrational cube root. Show your work. Note: You will find the option to add a cubic root symbol in the Algebra (x) keyboard.

Answer 1

To rewrite the irrational cube root root(189, 3) as the product of an integer and another irrational cube root, we first need to factorize 189.

The prime factorization of 189 is:
189 = 3^3 × 7

Now, we can rewrite root(189, 3) as the product of the cube root of the perfect cube part and the cube root of the remaining part:

root(189, 3) = root(3^3, 3) × root(7, 3)

Simplifying,

root(3^3, 3) × root(7, 3) = 3 × root(7, 3)

Therefore, the irrational cube root root(189, 3) can be rewritten as the product of 3 and root(7, 3).