Question

Which of the following is equivalent to

Answer 1

None of the above! It’s 5b times cube root of a squared. The first option is close, but when you bring the b out of the root it loses the cube!

Answer 2

Explanation:

To solve this, we need to remember that when you multiplicate two roots you can multiply the numbers inside the two roots and put them inside just one root.

So in this case we have ∛5ab² ·∛25ab

We are going to multiply the numbers inside the roots and we get

∛5ab²·25ab = ∛75a²b³

But 75 = 5³ so we have

∛75a²b³ = ∛5³a²b³

Since we have powers of 3 inside the root, we can take them outside the root with the exponent divided by 3.

∛5³a²b³ = 5b∛a²

Thus, the correct answer is a) 5b∛a²