Rationalize the denominator and simplify.
-$\frac{\sqrt{2}}{\sqrt{7}+5}$

A) $\frac{\sqrt{14}+5 \sqrt{2}}{-18}$

B) $\frac{\sqrt{14}-5 \sqrt{2}}{12}$

C) $\frac{3 \sqrt{14}+7 \sqrt{2}}{35}$

D) $\frac{\sqrt{14}-5 \sqrt{2}}{-18}$

Question

Rationalize the denominator and simplify.
-$\frac{\sqrt{2}}{\sqrt{7}+5}$

A) $\frac{\sqrt{14}+5 \sqrt{2}}{-18}$

B) $\frac{\sqrt{14}-5 \sqrt{2}}{12}$

C) $\frac{3 \sqrt{14}+7 \sqrt{2}}{35}$

D) $\frac{\sqrt{14}-5 \sqrt{2}}{-18}$

Quizplus · Accepted Answer

To rationalize the denominator of $\frac{\sqrt{2}}{\sqrt{7}+5}$, multiply both the numerator and the denominator by the conjugate of the denominator, which is $\sqrt{7}-5$. This results in $\frac{\sqrt{2}(\sqrt{7}-5)}{(\sqrt{7}+5)(\sqrt{7}-5)}$, simplifying to $\frac{\sqrt{14}-5\sqrt{2}}{7-25}$, which further simplifies to $\frac{\sqrt{14}-5\sqrt{2}}{-18}$.

Rationalize the Denominator and Simplify 27+5\frac{\sqrt{2}}{\sqrt{7}+5}7​+52​​ A) 14+52−18\frac{\sqrt{14}+5 \sqrt{2}}{-18}−1814​+52​​ B) 14−5212\frac{\sqrt{14}-5 \sqrt{2}}{12}1214​−52​​ C) 314+7235\frac{3 \sqrt{14}+7 \sqrt{2}}{35}35314​+72​​

Rationalize the Denominator and Simplify $\frac{\sqrt{2}}{\sqrt{7}+5}$ A) $\frac{\sqrt{14}+5 \sqrt{2}}{-18}$ B) $\frac{\sqrt{14}-5 \sqrt{2}}{12}$ C) $\frac{3 \sqrt{14}+7 \sqrt{2}}{35}$