Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$\frac { 3 } { \sqrt { 125 x } }$
A) $\frac { \sqrt { 15 x } } { 25 x }$
B) $\frac { 3 \sqrt { 125 x } } { 125 x }$
C) $\frac { 3 \sqrt { 5 x } } { 25 x }$
D) $\frac { 3 \sqrt { x } } { 5 x }$

Question

Quizplus · Accepted Answer

To rationalize the denominator of $\frac { 3 } { \sqrt { 125 x } }$, multiply both the numerator and the denominator by $\sqrt { 125 x }$. This gives $\frac { 3 \sqrt { 125 x } } { 125 x }$. Simplifying $\sqrt { 125 x }$ to $\sqrt { 25 \cdot 5 \cdot x }$ = $5\sqrt { 5x }$, the expression becomes $\frac { 3 \cdot 5\sqrt { 5x } } { 125 x }$ = $\frac { 3 \sqrt { 5 x } } { 25 x }$.

Rationalize the Denominator and Simplify 3125x\frac { 3 } { \sqrt { 125 x } }125x​3​

Rationalize the Denominator and Simplify $\frac { 3 } { \sqrt { 125 x } }$