Question

Rewrite the irrational cube root ^3divided by 189 as the product of an integer and another irrational cube root.

Answer 1

Let's rewrite the expression in the desired form.

To find an integer that can be factored out, let's factorize 189:
189 = 3 * 63

We can rewrite the expression as follows:
(cube root of 3^3 * 63) / 189

Now, let's simplify the cube root:

(cube root of 3^3 * 63) = cube root of (27 * 63)
= cube root of (1701)

Now, let's rewrite the expression using the integer factor and the simplified cube root:

(cube root of 3^3 * 63) / 189 = (cube root of 1701) / (3 * 63 / 189)
= (cube root of 1701) / (1 * 1)
= (cube root of 1701) / 1

Therefore, the irrational cube root (^3) divided by 189 can be rewritten as the product of an integer (1) and another irrational cube root (cube root of 1701).