Question

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

Answer 1

can you condense the answer to be a small as it can be while also being as good as this

Answer 2

To rewrite the irrational cube root ^3√189 as the product of an integer and another irrational cube root, we need to find a perfect cube that can be factored out from 189.

To do this, we can look for the largest perfect cube that is a factor of 189. The largest perfect cube that is less than 189 is 27 (which is equal to 3^3).

So, we can write 189 as: 189 = 27 * 7.

Now, let's express this in terms of cube roots:

^3√189 = ^3√(27 * 7)

Taking the cube root of 27 (which is 3), we can rewrite this as:

^3√189 = 3 * ^3√7

Therefore, the irrational cube root ^3√189 can be rewritten as the product of the integer 3 and the irrational cube root ^3√7.

Answer 3

Certainly! The irrational cube root ^3√189 can be rewritten as 3√7, where 3 is an integer and √7 is another irrational cube root.