Question

What is the following sum

Answer 1

second option: 12b²(∛2a)

Explanation:

you can break
`\sqrt[3]{54a}` into
`\sqrt[3]{3^3(2a)}` which equals 3
`\sqrt[3]{2a}`

you can break
`\sqrt[3]{2ab^6}` into
`\sqrt[3]{2ab^3b^3}` which equals b²
`\sqrt[3]{2a}`

now we can simplify: (3b² · 3
`\sqrt[3]{2a}`) + 3b²
`\sqrt[3]{2a}` = 9b²
`\sqrt[3]{2a}` + 3b²
`\sqrt[3]{2a}`

this equals 12b²
`\sqrt[3]{2a}`

Answer 2

2nd option is the correct answer

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

Explanation:

`3 {b}^(2) \bigg( \sqrt[3]{54a} \bigg) + 3 \bigg( \sqrt[3]{2a {b}^(6) } \bigg) \\ \\ = 3 {b}^(2) \bigg( \sqrt[3]{27 * 2a} \bigg) + 3 \bigg( \sqrt[3]{2a {( {b}^(2) )}^(3) } \bigg) \\ \\ = 3 {b}^(2) \bigg( \sqrt[3]{ {3}^(3) * 2a} \bigg) + 3 \bigg({\sqrt[3]{{( {b}^(2) )}^(3)2a} } \bigg) \\ \\ = 3 {b}^(2) * 3 \sqrt[ 3]{2a} + 3 {b}^(2) \sqrt[3]{2a} \\ \\ = 9 {b}^(2) \sqrt[ 3]{2a} + 3 {b}^(2) \sqrt[3]{2a} \\ \\ = 12{b}^(2) \bigg(\sqrt[3]{2a} \bigg)`