Question

Rationalize the denominator of $\frac{1}{8+2\sqrt{5}}$

• A. (4-√5)/20
• B. (4-√5)/22
• C. (5-√5)/20
• D. (5-√5)/22

Answer 1

The correct option is B

(4-√5)/22

$\frac{1}{8+2\sqrt{5}}$=$\frac{8-2\sqrt{5}}{(8+2\sqrt{5})8-2\sqrt{5}}$=$\frac{8-2\sqrt{5}}{64-20}$=$\frac{4-\sqrt{5}}{22}$