Question

What is the irrational cube root ^3√48 rewritten as a product of an integer and another irrational cube root?

Answer 1

To find an integer and another irrational cube root equivalent to ^3√48, we can express 48 as a product of its prime factors:

48 = 2 * 2 * 2 * 2 * 3

Now, we look for cubes among these prime factors. In this case, we have two cubes: 2 * 2 * 2 = (2^3) = 8.

So, we can rewrite ^3√48 as ^3√(8 * 2 * 3).

Taking the cube root of 8 gives us 2:

^3√(8 * 2 * 3) = 2 * ^3√(2 * 3)

Therefore, the irrational cube root ^3√48 can be rewritten as the product 2 * ^3√(6).