Question

Simplify by rationalising the denominator: $\frac{5+\sqrt{6}}{5-\sqrt{6}}$

• A. $\frac{31+10\sqrt{6}}{31}$
• B. $\frac{31-10\sqrt{6}}{19}$
• C. $\frac{31-10\sqrt{6}}{31}$
• D. $\frac{31+10\sqrt{6}}{19}$

Answer 1

The correct option is D $\frac{31+10\sqrt{6}}{19}$

As given $\frac{5+\sqrt{6}}{5-\sqrt{6}}$
Multiplying the numerator and denominator by the conjugate of $5-\sqrt{6}$ we get
$=\frac{5+\sqrt{6}}{5-\sqrt{6}}\times \frac{5+\sqrt{6}}{5+\sqrt{6}}$
$=\frac{{(5+\sqrt{6})}^2}{{\left(5\right)}^2-{\left(\sqrt{6}\right)}^2}$
$=\frac{25+6+2\times 5\times \sqrt{6}}{25-6}$
$=\frac{31+10\sqrt{6}}{19}$