Question

If $\sqrt{5}=2.236$ and $\sqrt{6}=2.449$, find the value of $\frac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{1-\sqrt{2}}{\sqrt{5}-\sqrt{3}}$

• A. $0.213$
• B. $-0.213$
• C. $-1.213$
• D. $1.213$

Answer 1

The correct option is B $-0.213$

As Given $\frac{1+\sqrt{2}}{\sqrt{5}+\sqrt{3}}+\frac{1-\sqrt{2}}{\sqrt{5}-\sqrt{3}}$
$=\frac{(1+\sqrt{2})(\sqrt{5}-\sqrt{3})+(1-\sqrt{2})(\sqrt{5}+\sqrt{3})}{(\sqrt{5}-\sqrt{3})(\sqrt{5}+\sqrt{3})}$
$=\frac{\sqrt{5}+\sqrt{2}\sqrt{5}-\sqrt{3}-\sqrt{2}\sqrt{3}+\sqrt{5}-\sqrt{2}\sqrt{5}+\sqrt{3}-\sqrt{2}\sqrt{3}}{5-3}$
$=\frac{2\sqrt{5}-2\sqrt{6}}{2}$
$=\frac{2(\sqrt{5}-\sqrt{6})}{2}$
$\sqrt{5}-\sqrt{6}$
As given $\sqrt{5}=2.236,\sqrt{6}=2.449$
$2.236-2.449=-0.213$