Question

Rationalize the denominator

$\frac{1}{(\sqrt{7}-\sqrt{6})}$

• A. $\sqrt{7}+\sqrt{6}$
• B. $\sqrt{7}-\sqrt{6}$
• C. $-\sqrt{7}+\sqrt{6}$
• D. $\sqrt{6}-\sqrt{7}$

Answer 1

The correct option is A

$\sqrt{7}+\sqrt{6}$

$\frac{1}{\sqrt{7}-\sqrt{6}}$

$=\frac{1(\sqrt{7}+\sqrt{6})}{(\sqrt{7}-\sqrt{6})(\sqrt{7}+\sqrt{6})}$

$=\frac{\sqrt{7}+\sqrt{6}}{(\sqrt{7}{)}^2-(\sqrt{6}{)}^2}$

$=\frac{\sqrt{7}+\sqrt{6}}{1}$

$=\sqrt{7}+\sqrt{6}$