Rewrite the irrational cube root of 189 as the product of an integer and another irrational square root. Show your work
To rewrite the cube root of 189 as the product of an integer and another irrational square root, we first need to find a perfect cube that divides 189.
The prime factorization of 189 is:
189 = 3^3 * 7
Therefore, the cube root of 189 can be rewritten as:
∛189 = ∛(3^3 * 7) = 3∛7
So, the cube root of 189 can be written as the product of the integer 3 and the irrational square root √7:
3√7