Question

Rationalise the denominator of $\frac{1}{5+\sqrt{3}}$

• A. $\frac{5-\sqrt{3}}{16}$
• B. $\frac{5+\sqrt{3}}{16}$
• C. $\frac{2}{5+\sqrt{3}}$
• D. None of these

Answer 1

The correct option is A $\frac{5-\sqrt{3}}{16}$

To rationalise the denominator, is to make the denominator a rational number which can be done by multiplying and dividing the number by
$\frac{1}{5+\sqrt{3}}\times \frac{5-\sqrt{3}}{5-\sqrt{3}}=\frac{5-\sqrt{3}}{25-9}$
$=\frac{5-\sqrt{3}}{16}$