Rationalize the denominator and simplify. Assume that all variables represent positive real numbers.
-$$\frac { 2 } { 8 - \sqrt { 5 } }$$
A) $\frac { 2 } { 8 } - \frac { 2 } { \sqrt { 5 } }$
B) $\frac { 16 - 2 \sqrt { 5 } } { 59 }$
C) $\frac { 16 + 2 \sqrt { 5 } } { - 3 }$
D) $\frac { 16 + 2 \sqrt { 5 } } { 59 }$

Question

Quizplus · Accepted Answer

To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator, $8 + \sqrt{5}$. This results in $\frac{2(8 + \sqrt{5})}{(8 - \sqrt{5})(8 + \sqrt{5})}$. Simplifying the denominator gives $64 - 5 = 59$, and the numerator becomes $16 + 2\sqrt{5}$, leading to $\frac{16 + 2\sqrt{5}}{59}$.

Rationalize the Denominator and Simplify 28−5\frac { 2 } { 8 - \sqrt { 5 } }8−5​2​

Rationalize the Denominator and Simplify $\frac { 2 } { 8 - \sqrt { 5 } }$