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

Accepted Solution

ANSWERThe correct answer is BEXPLANATIONThe given sum is [tex] \sqrt{ {x}^{2} {y}^{3} } + 2 \sqrt{ {x}^{3} {y}^{4} } + xy \sqrt{y} [/tex]We need to remove the perfect squares.[tex]\sqrt{ {x}^{2} \times {y}^{2} \times y } + 2 \sqrt{ {x}^{2} \times ( {y}^{2})^{2} \times x } + xy \sqrt{y} [/tex]Let us split the radical sign for the factors to get;[tex]\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} [/tex]This simplifies to[tex]xy \sqrt{y} + 2x {y}^{2} \sqrt{x} + xy \sqrt{y} [/tex]Group similar terms to get:[tex]xy\sqrt{y} + xy \sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]Combine the similar terms to get:[tex]2xy\sqrt{y} + 2x {y}^{2} \sqrt{x} [/tex]The correct answer is B.