Question

Rationalise the denominator of $\frac{1}{\sqrt{5}-\sqrt{2}}$

• A. $\frac{1}{3}(\sqrt{5}+\sqrt{2})$
• B. $(\sqrt{5}+\sqrt{2})$
• C. $(\sqrt{5}-\sqrt{2})$
• D. $\frac{1}{3}(\sqrt{5}-\sqrt{2})$
  

Answer 1

Answer: (A)

$\frac{1}{3}(\sqrt{5}+\sqrt{2})$

As given $\frac{1}{\sqrt{5}-\sqrt{2}}$
Now multiply and divide by $\sqrt{5}+\sqrt{2}$
$=\frac{1}{\sqrt{5}-\sqrt{2}}\times \frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}}$
$=\frac{\sqrt{5}+\sqrt{2}}{{\left(\sqrt{5}\right)}^2-{\left(\sqrt{2}\right)}^2}$
$=\frac{\sqrt{5}+\sqrt{2}}{5-2}$
$=\frac{1}{3}\sqrt{5}+\sqrt{2}$