Question

if root 2 = 1.414 and root 5= 2.236, find the value of root 10 - root 5 divided by 2 root 2 upto three places of decimals.

Answer 1

$$\begin{gathered} \sqrt{2}=1.414\mathrm{and}\sqrt{5}=2.236\left[\mathbf{given}\right] \\ \mathrm{Now},\frac{\sqrt{10}-\sqrt{5}}{2\sqrt{2}} \\ =\frac{\left(\sqrt{10}-\sqrt{5}\right)\times \sqrt{2}}{2\sqrt{2}\times \sqrt{2}} \\ =\frac{\sqrt{20}-\sqrt{10}}{4} \\ =\frac{\sqrt{4\times 5}-\sqrt{2\times 5}}{4} \\ =\frac{2\sqrt{5}-\sqrt{2}\times \sqrt{5}}{4} \\ =\frac{\sqrt{5}\left(2-\sqrt{2}\right)}{4} \\ =\frac{2.236\left(2-1.414\right)}{4} \\ =\frac{2.236\times 0.586}{4}=\frac{1.310296}{4}=0.3275 \end{gathered}$$