Question

find the value of 3 / root 5 + root 2 + 7 / root 5 minus root 2 ,if root 5 is equal to 2.2 36 and root 2 is equal to 1.414

Answer 1

$$\begin{gathered} \frac{3}{\sqrt{5}+\sqrt{2}}+\frac{7}{\sqrt{5}{\displaystyle }{\displaystyle -}{\displaystyle }{\displaystyle \sqrt{2}}} \\ =\frac{3\sqrt{5}-3\sqrt{2}+7\sqrt{5}+7\sqrt{2}}{\left(\sqrt{5}+\sqrt{2}\right){\displaystyle \left(\sqrt{5}-\sqrt{2}\right)}} \\ =\frac{10\sqrt{5}+4\sqrt{2}}{5-2}\left[\mathbf{as}\mathbf{,}\mathbf{}\left(\mathbf{a}\mathbf{+}\mathbf{b}\right)\left(\mathbf{a}\mathbf{-}\mathbf{b}\right)\mathbf{}\mathbf{=}\mathbf{}{\mathbf{a}}^{\mathbf{2}}\mathbf{}\mathbf{-}\mathbf{}{\mathbf{b}}^{\mathbf{2}}\right] \\ =\frac{10\sqrt{5}+4\sqrt{2}}{3} \\ =\frac{10\times 2.236+4\times 1.414}{3} \\ =\frac{22.36+5.656}{3} \\ =\frac{28.016}{3} \\ =9.339 \end{gathered}$$