Find the value to three places of decimals of each of the following. It is given that $\sqrt{2}=1.414,\sqrt{3}=1.732,\sqrt{5}=2.236$ and $\sqrt{10}=3.162$
$\frac{\sqrt{10}+\sqrt{15}}{\sqrt{2}}$

Solution:-

Given that:-

$\sqrt{2}=1.414$

$\sqrt{3}=1.732$

$\sqrt{5}=2.236$

$\sqrt{10}=3.162$

$\therefore \frac{\sqrt{10}+\sqrt{15}}{\sqrt{2}}$

$\Rightarrow =\frac{\sqrt{10}+\sqrt{3.5}}{\sqrt{2}}$

$\Rightarrow =\frac{\sqrt{10}+\sqrt{3}.\sqrt{5}}{\sqrt{2}}$

$\Rightarrow =\frac{3.162+(1.732\times 2.236)}{1.414}$

$\Rightarrow =\frac{3.162+3.872752}{1.414}$

$\Rightarrow =\frac{7.034752}{1.414}$

$\Rightarrow =4.9750721\approx 4.975$

Hence, the correct answer is $4.975$.