What is the irrational cube root ^3√40 rewritten as a product of an integer and another irrational cube root?

Question

1. 2 ^3√5
2. 2 ^3√10
3. 8 ^3√5
4. -2 ^3√5

Answer 1

The answer is option 3, 8 ^3√5.

To see why, we can simplify the expression ^3√40. The cube root of 40 can be written as 40^(1/3).

To rewrite 40 as a product of an integer and another cube root, we can factorize 40. We notice that 40 can be written as 8 * 5.

So, 40^(1/3) = (8 * 5)^(1/3) = 8^(1/3) * 5^(1/3) = 8 ^3√5.

Therefore, the expression ^3√40 can be rewritten as a product of an integer (8) and another irrational cube root ( ^3√5).