Question

What is the following sum?
3b^2(^3 √54a) + 3(^3 √2ab^6)

Answer 1

`12b^2\sqrt[3]{2a}`

Explanation:

Our original expression is

`3b^2(\sqrt[3]{54a})+3(\sqrt[3]{2ab^6})`

We will first expand the terms under the cubed roots:

`3b^2(\sqrt[3]{3*3*3*2*a})+3(\sqrt[3]{2a*b*b*b*b*b*b})`

Since we have cubed roots, we are looking for groups of 3 factors. In the first term, we have three 3's; this means we can bring a 3 out. In the second term, we have six b's; this means we can bring out 2 b's:

`3b^2(3\sqrt[3]{2a})+3(b^2\sqrt[3]{2a})\\\\=9b^2\sqrt[3]{2a}+3b^2\sqrt[3]{2a}`

Lastly, combine like terms:

`12b^2\sqrt[3]{2a}`

Answer 2

`12b^(2) \sqrt[3]{2a}`

Explanation: