Question

Find the value of $\frac{\sqrt{10}-\sqrt{5}}{2\sqrt{2}}$ upto three decimal places. (take $\sqrt{2}=1.414$ and $\sqrt{5}=2.236$)

• A. $0.278$
• B. $0.296$
• C. $0.328$
• D. $0.363$

Answer 1

Answer: (C)

$0.328$

$\frac{\sqrt{10}-\sqrt{5}}{2\sqrt{2}}\times \frac{\sqrt{2}}{\sqrt{2}}$

$=\frac{\sqrt{20}-\sqrt{10}}{4}$

$=\frac{\sqrt{4\times 5}-\sqrt{2}\sqrt{5}}{4}$

$=\frac{2\sqrt{5}-\sqrt{2}\times \sqrt{5}}{4}$

$=\frac{\sqrt{5}\left(2-\sqrt{2}\right)}{4}$

$=\frac{2.236\left(2-1.414\right)}{4}$

$=\frac{2.236\times 0.586}{4}$

$=0.328$