Question

What is the following sum? Assume.. (look at picture)

Answer 1

The correct answer is B

Step-by-step explanation

The given sum is

`\sqrt{ {x}^(2) {y}^(3) } + 2 \sqrt{ {x}^(3) {y}^(4) } + xy √(y)`

We need to remove the perfect squares.

`\sqrt{ {x}^(2) * {y}^(2) * y } + 2 \sqrt{ {x}^(2) * ( {y}^(2))^(2) * x } + xy √(y)`

Let us split the radical sign for the factors to get;

`\sqrt{ {x}^(2)} * \sqrt{ {y}^(2)} * √(y) + 2 \sqrt{ {x}^(2) } * \sqrt{( {y}^(2))^(2)} * √(x) + xy √(y)`

This simplifies to

`xy √(y) + 2x {y}^(2) √(x) + xy √(y)`

Group similar terms to get:

`xy√(y) + xy √(y) + 2x {y}^(2) √(x)`

Combine the similar terms to get:

`2xy√(y) + 2x {y}^(2) √(x)`

The correct answer is B.