Question

rewrite the irrational cube root ^3√189 as the product of an integer and another irrational cube root.

Answer 1

[AI-generated answer — Bot GPT 3.5]

Since 189 is not a perfect cube, we can't express ^3√189 as a single irrational cube root. However, we can express it as the product of an integer and another irrational cube root.

To do this, we need to find a perfect cube that is a factor of 189. The largest perfect cube that is a factor of 189 is 27 (which is equal to 3^3). So we can rewrite ^3√189 as:

^3√189 = ^3√(27 * 7)

Now, we can break this down further:

^3√(27 * 7) = ^3√27 * ^3√7

Since ^3√27 equals 3 and ^3√7 is still an irrational cube root, we can rewrite the expression as:

^3√189 = 3 * ^3√7

Therefore, ^3√189 can be expressed as the product of an integer (3) and another irrational cube root (√7).