Rationalize the denominator and simplify. Assume all variables represent nonnegative real numbers.
-$\frac { 3 \sqrt { 26 x } } { \sqrt { x ^ { 3 } } }$
A) $\frac { 3 \sqrt { 26 x } } { x }$
B) $3 \times \sqrt { 26 }$
C) $\frac { 3 \sqrt { 26 } } { x }$
D) $\frac { 78 } { x }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, we can multiply both the numerator and denominator by $\sqrt{x}$. This gives us:
$$\frac{3\sqrt{26x}\cdot\sqrt{x}}{\sqrt{x^3}\cdot \sqrt{x}}=\frac{3\sqrt{26x^2}}{\sqrt{x^4}}=\frac{3\sqrt{26}}{x^2}=\frac{3\sqrt{26}}{x}\cdot\frac{1}{x}=\frac{3\sqrt{26}}{x}.$$ Therefore, the correct choice is C.

Rationalize the Denominator and Simplify 326xx3\frac { 3 \sqrt { 26 x } } { \sqrt { x ^ { 3 } } }x3​326x​​

Rationalize the Denominator and Simplify $\frac { 3 \sqrt { 26 x } } { \sqrt { x ^ { 3 } } }$