Question

What is the following sum 2{^3 square root 16x^3y}+4{^3 square root 54x^6y^5}?

Answer 1

B: 4x(
`\sqrt[3]{2}`y) + 12
`x^(2)`y (
`\sqrt[3]{2}`
`y^(2)`)

Explanation:

took the test

Answer 2

`4x\sqrt[3]{2y}` +
`12x^2y\sqrt[3]{2y^2}`

Explanation:

Given expression
`3\sqrt[3]{16x^3y} + 4\sqrt[3]{54x^6y^5}`.

Let us simplify each of the radical separately first.

`3\sqrt[3]{16x^3y}=3\sqrt[3]{2* 8 * x^3* y} =2\sqrt[3]{2} * \sqrt[3]{8} * \sqrt[3]{x^3} * \sqrt[3]{y}`

`=2\sqrt[3]{2} * 2* x* \sqrt[3]{y}`

=
`2* 2* x\sqrt[3]{2y}`

`= 4x\sqrt[3]{2y}`

`4\sqrt[3]{54x^6y^5}=4\sqrt[3]{2* 27 * x^3* x^3 * y^3* y^2} =4\sqrt[3]{2} * \sqrt[3]{27} * \sqrt[3]{x^3} * \sqrt[3]{x^3} * \sqrt[3]{y^3}*\sqrt[3]{y^2}`

`=4\sqrt[3]{2} * 3 * x* x * y * \sqrt[3]{y^2}`

`=12x^2y\sqrt[3]{2y^2}`

Therefore,

`3\sqrt[3]{16x^3y} + 4\sqrt[3]{54x^6y^5}` =
`4x\sqrt[3]{2y}` +
`12x^2y\sqrt[3]{2y^2}`