Rewrite the irrational cube root 189−−−√3 as the product of an integer and another irrational cube root. Show your work.

Answer 1

To rewrite the irrational cube root 189√3 as the product of an integer and another irrational cube root, we need to find a perfect cube factor of 189.

We know that 189 = 3 * 3 * 3 * 7. Since 3 is a perfect cube, we can rewrite 189 as 3^3 * 7.

Therefore, we can rewrite the cube root of 189 as:

3√(189) = 3√(3^3 * 7)
= 3 * 3√7

So, the irrational cube root 189√3 can be written as 3 times the cube root of 7: 3 * 3√7.