Question

simplify 4 root of 6 +5 root of 32 -7 root of 128 + root of 162 - root of 722

Answer 1

$$\begin{gathered} 4\sqrt{6}+5\sqrt{32}-7\sqrt{128}+\sqrt{162}-\sqrt{722} \\ =4\sqrt{6}+5\sqrt{2\times 2\times 2\times 2\times 2}-7\sqrt{2\times 2\times 2\times 2\times 2\times 2\times 2}+\sqrt{2\times 3\times 3\times 3\times 3}-\sqrt{2\times 19\times 19} \\ =4\sqrt{6}+5\times 2\times 2\sqrt{2}-7\times 2\times 2\times 2\sqrt{2}+3\times 3\sqrt{2}-19\sqrt{2} \\ =4\sqrt{6}+20\sqrt{2}-56\sqrt{2}+9\sqrt{2}-19\sqrt{2} \\ =4\sqrt{6}+29\sqrt{2}-75\sqrt{2} \\ =4\sqrt{6}-46\sqrt{2} \end{gathered}$$