Question

The expression $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ when simplified reduces to $a-b\sqrt{15}$

Then a + b is

• A. 15
• B. 10
• C. 20
• D. 5

Answer 1

The correct option is D

5

In $\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$ the denominator has to be rationalised for simplification. So ,

$\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}$$\times$$\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}-\sqrt{3}}$
$=\frac{(\sqrt{5}-\sqrt{3}{)}^2}{{\sqrt{5}}^2-{\sqrt{3}}^2}$
$=\frac{1}{2}[{\left(\sqrt{5}\right)}^2+{\left(\sqrt{3}\right)}^2-2\sqrt{15}]$
$=4-\sqrt{15}$
$\text{So, a=4 and b=1.}$
$a+b=5$