Question

simplify root 125 - 4 root 6 + root 294 -2 root 1/6

Answer 1

$$\begin{gathered} \sqrt{125}-4\sqrt{6}+\sqrt{294}-2\sqrt{\frac{1}{6}} \\ =\sqrt{5\times 5\times 5}-4\sqrt{6}+\sqrt{2\times 3\times 7\times 7}-2\times \frac{\sqrt{6}}{6} \\ =5\sqrt{5}-4\sqrt{6}+7\sqrt{6}-\frac{\sqrt{6}}{3} \\ =\frac{15\sqrt{5}-12\sqrt{6}+21\sqrt{6}-\sqrt{6}}{3} \\ =\frac{15\sqrt{5}+8\sqrt{6}}{3} \end{gathered}$$