Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\sqrt { \frac { 75 x ^ { 3 } } { y 5 } }$
A) $\frac { x \sqrt { 75 x y } } { y 3 }$
B) $\frac { 5 x ^ { 3 } \sqrt { 3 } } { y 5 }$
C) $\frac { 5 x } { y 2 } \sqrt { \frac { 3 x } { y } }$
D) $\frac { 5 x \sqrt { 3 x y } } { y 3 }$

Question

Quizplus · Accepted Answer

First, simplify the expression inside the square root:
$$\sqrt{\frac{75x^3}{y^5}} = \sqrt{\frac{3 \cdot 25 x^2 \cdot x}{y^2 \cdot y^3}} = \sqrt{\frac{3 \cdot 25 x^2}{y^2} \cdot \frac{x}{y^3}} = \frac{5x}{y^2} \sqrt{\frac{3x}{y}}$$
Then, rationalize the denominator:
$$\frac{5x \sqrt{3xy}}{y^3}$$ Thus, the correct answer is (D).

Rationalize the Denominator and Simplify 75x3y5\sqrt { \frac { 75 x ^ { 3 } } { y 5 } }y575x3​​

Rationalize the Denominator and Simplify $\sqrt { \frac { 75 x ^ { 3 } } { y 5 } }$