Simplify by rationalizing the denominator.
-$\frac { 5 } { \sqrt { 10 } + \sqrt { 15 } }$
A) $\sqrt { 15 } + \sqrt { 10 }$
B) $\sqrt { 5 }$
C) $\sqrt { 15 } - \sqrt { 10 }$
D) $\sqrt { 10 } - \sqrt { 15 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator, $\sqrt{10} - \sqrt{15}$. This results in $\frac{5(\sqrt{10} - \sqrt{15})}{(\sqrt{10} + \sqrt{15})(\sqrt{10} - \sqrt{15})}$. The denominator simplifies to $10 - 15 = -5$, and the expression simplifies to $\sqrt{15} - \sqrt{10}$.

Simplify by Rationalizing the Denominator 510+15\frac { 5 } { \sqrt { 10 } + \sqrt { 15 } }10​+15​5​

Simplify by Rationalizing the Denominator $\frac { 5 } { \sqrt { 10 } + \sqrt { 15 } }$