Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\sqrt { \frac { 45 x ^ { 3 } } { y 5 } }$
A) $\frac { 3 x } { y 2 } \sqrt { \frac { 5 x } { y } }$
B) $\frac { x \sqrt { 45 x y } } { y 3 }$
C) $\frac { 3 x \sqrt { 5 x y } } { y 3 }$
D) $\frac { 3 x ^ { 3 } \sqrt { 5 } } { y 5 }$

Question

Quizplus · Accepted Answer

We can simplify the expression as follows:

$$\sqrt{\frac{45x^3}{y^5}} = \sqrt{\frac{9\cdot 5\cdot x^2\cdot x}{y^2\cdot y^3}} = 3\cdot\sqrt{\frac{5x}{y^2}}$$

Now we can rationalize the denominator by multiplying both the numerator and denominator by $y$:

$$3\cdot\sqrt{\frac{5x}{y^2}} = \frac{3x\sqrt{5xy^2}}{(y^2)^{3/2}} = \frac{3x\sqrt{5xy}}{y^3}$$

Thus, the best choice is $\boxed{\textbf{(C)}}$.

Rationalize the Denominator and Simplify 45x3y5\sqrt { \frac { 45 x ^ { 3 } } { y 5 } }y545x3​​

Rationalize the Denominator and Simplify $\sqrt { \frac { 45 x ^ { 3 } } { y 5 } }$