Question

If $\frac{4+3\sqrt{5}}{\sqrt{5}}=a+b\sqrt{5}$ then, the value of $b$ is

• A. $\frac{3}{5}$
• B. $\frac{4}{5}$
• C. $\frac{3\sqrt{5}}{5}$
• D. $\frac{2}{5}$

Answer 1

The correct option is B $\frac{4}{5}$

$\frac{4+3\sqrt{5}}{\sqrt{5}}=a+b\sqrt{5}$
$\frac{(4+3\sqrt{5})\sqrt{5}}{\sqrt{5}\times \sqrt{5}}=\frac{4\sqrt{5}+15}{5}=\frac{4\sqrt{5}}{5}+\frac{15}{5}$
$=3+\frac{4\sqrt{5}}{5}$
Clearly, $a=3$
$b=\frac{4}{5}$.