Question

Find the value of $\frac{\sqrt{10}-\sqrt{15}}{2\sqrt{5}}$ upto three decimal places. (take $\sqrt{2}=1.414$ and $\sqrt{3}=1.732$)

Answer 1

Given: $\frac{\sqrt{10}-\sqrt{15}}{2\sqrt{5}}$

multiplying and dividing by $2\sqrt{5}$

$=\frac{2\sqrt{5}\times (\sqrt{10}-\sqrt{15})}{2\sqrt{5}\times 2\sqrt{5}}$

$=\frac{2\sqrt{50}-2\sqrt{75}}{20}$

$=\frac{\sqrt{50}-\sqrt{75}}{10}$

$=\frac{5\sqrt{2}-5\sqrt{3}}{10}$

$=\frac{5(1.414-1.732)}{10}$

$=\frac{5\times -0.318}{10}$

$=-\frac{1.59}{10}$

$=-0.159$