Question

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

Answer 1

ANSWER

The correct answer is B

EXPLANATION

The given sum is

$\sqrt{ {x}^{2} {y}^{3} } + 2 \sqrt{ {x}^{3} {y}^{4} } + xy \sqrt{y}$

We need to remove the perfect squares.

$\sqrt{ {x}^{2} \times {y}^{2} \times y } + 2 \sqrt{ {x}^{2} \times ( {y}^{2})^{2} \times x } + xy \sqrt{y}$

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

$\sqrt{ {x}^{2}} \times \sqrt{ {y}^{2}} \times \sqrt{y} + 2 \sqrt{ {x}^{2} } \times \sqrt{( {y}^{2})^{2}} \times \sqrt{x} + xy \sqrt{y}$

This simplifies to

$xy \sqrt{y} + 2x {y}^{2} \sqrt{x} + xy \sqrt{y}$

Group similar terms to get:

$xy\sqrt{y} + xy \sqrt{y} + 2x {y}^{2} \sqrt{x}$

Combine the similar terms to get:

$2xy\sqrt{y} + 2x {y}^{2} \sqrt{x}$

The correct answer is B.