Question

Simplify:(4 root 3 / 2- 2 root 2) - (30/ 4 root 3 -3 root 2) - (3 root 2 / 3+ 2 root 3)

Answer 1

Answer :

Simplify : $\frac{4\sqrt{3}}{2-2\sqrt{2}}-\frac{30}{4\sqrt{3}-3\sqrt{2}}-\frac{3\sqrt{2}}{3+2\sqrt{3}}$ , So

$$\begin{gathered} \Rightarrow \frac{4\sqrt{3}}{2-2\sqrt{2}}\times \frac{2+2\sqrt{2}}{2+2\sqrt{2}}-\frac{30}{4\sqrt{3}-3\sqrt{2}}\times \frac{4\sqrt{3}+3\sqrt{2}}{4\sqrt{3}+3\sqrt{2}}-\frac{3\sqrt{2}}{3+2\sqrt{3}}\times \frac{3-2\sqrt{3}}{3-2\sqrt{3}} \\ \Rightarrow \frac{8\sqrt{3}+8\sqrt{6}}{2^2-{\left(2\sqrt{2}\right)}^2}-\frac{120\sqrt{3}+90\sqrt{2}}{{\left(4\sqrt{3}\right)}^2-{\left(3\sqrt{2}\right)}^2}-\frac{9\sqrt{2}-6\sqrt{6}}{3^2-{\left(2\sqrt{3}\right)}^2} \\ \Rightarrow \frac{8\sqrt{3}+8\sqrt{6}}{4-8}-\frac{120\sqrt{3}+90\sqrt{2}}{48-18}-\frac{9\sqrt{2}-6\sqrt{6}}{9-12} \\ \Rightarrow \frac{8\sqrt{3}+8\sqrt{6}}{-4}-\frac{120\sqrt{3}+90\sqrt{2}}{30}-\frac{9\sqrt{2}-6\sqrt{6}}{-3} \\ \Rightarrow \frac{4\left(2\sqrt{3}+2\sqrt{6}\right)}{-4}-\frac{30\left(4\sqrt{3}+3\sqrt{2}\right)}{30}-\frac{3\left(3\sqrt{2}-2\sqrt{6}\right)}{-3} \\ \Rightarrow \frac{\left(2\sqrt{3}+2\sqrt{6}\right)}{-1}-\frac{\left(4\sqrt{3}+3\sqrt{2}\right)}{1}-\frac{\left(3\sqrt{2}-2\sqrt{6}\right)}{-1} \\ \Rightarrow -\left(2\sqrt{3}+2\sqrt{6}\right)-\left(4\sqrt{3}+3\sqrt{2}\right)+\left(3\sqrt{2}-2\sqrt{6}\right) \\ \Rightarrow -2\sqrt{3}-2\sqrt{6}-4\sqrt{3}-3\sqrt{2}+3\sqrt{2}-2\sqrt{6} \\ \Rightarrow -6\sqrt{3}-4\sqrt{6} \\ \mathbf{\Rightarrow }\mathbf{-}\mathbf{2}\sqrt{\mathbf{3}}\left(\mathbf{}\mathbf{3}\mathbf{}\mathbf{+}\mathbf{2}\mathbf{}\sqrt{\mathbf{2}}\right)\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{}\mathbf{(}\mathbf{}\mathit{A}\mathit{n}\mathit{s}\mathbf{}\mathbf{)} \end{gathered}$$