Question

If $\sqrt{2}=1.414,$ then find the value of $\sqrt{6}-\sqrt{3}$ upto three places of decimal.

Answer 1

$\sqrt{2}=1.414$

$\sqrt{6}-\sqrt{3}=\sqrt{2\times 3}-\sqrt{3}$

$=\sqrt{3}\times \sqrt{2}-\sqrt{3}$

$=\sqrt{3}(\sqrt{2}-1)$

$=1.732(1.414-1)$

$=1.732\times 0.414=0.717$