Question

Simplify.

(i)$\frac{4}{7}\sqrt{147}+\frac{3}{8}\sqrt{192}-\frac{1}{5}\sqrt{75}$

(ii) $5\sqrt{3}+2\sqrt{27}+\frac{1}{\sqrt{3}}$

(iii) $\sqrt{216}-5\sqrt{6}+\sqrt{294}-\frac{3}{\sqrt{6}}$

(iv)$4\sqrt{12}-\sqrt{75}-7\sqrt{48}$


(v) $2\sqrt{48}-\sqrt{75}-\frac{1}{\sqrt{3}}$

Answer 1

(i) $\frac{4}{7}\sqrt{147}+\frac{3}{8}\sqrt{192}-\frac{1}{5}\sqrt{75}$

$$\begin{gathered} =\frac{4}{7}\sqrt{49\times 3}+\frac{3}{8}\sqrt{64\times 3}-\frac{1}{5}\sqrt{25\times 3} \\ =\frac{4}{7}\times 7\sqrt{3}+\frac{3}{8}\times 8\sqrt{3}-\frac{1}{5}\times 5\sqrt{3} \\ =4\sqrt{3}+3\sqrt{3}-\sqrt{3} \\ =6\sqrt{3} \end{gathered}$$

(ii) $5\sqrt{3}+2\sqrt{27}+\frac{1}{\sqrt{3}}$

$$\begin{gathered} =5\sqrt{3}+2\sqrt{9\times 3}+\frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}} \\ =5\sqrt{3}+6\sqrt{3}+\frac{\sqrt{3}}{3} \\ =11\sqrt{3}+\frac{\sqrt{3}}{3} \\ =\frac{33\sqrt{3}+\sqrt{3}}{3} \\ =\frac{34\sqrt{3}}{3} \end{gathered}$$

(iii) $\sqrt{216}-5\sqrt{6}+\sqrt{294}-\frac{3}{\sqrt{6}}$

$$\begin{gathered} =\sqrt{36\times 6}-5\sqrt{6}+\sqrt{49\times 6}-\frac{3}{\sqrt{6}}\times \frac{\sqrt{6}}{\sqrt{6}} \\ =6\sqrt{6}-5\sqrt{6}+7\sqrt{6}-\frac{3\sqrt{6}}{6} \\ =8\sqrt{6}-\frac{\sqrt{6}}{2} \\ =\frac{18\sqrt{6}-\sqrt{6}}{2} \\ =\frac{17\sqrt{6}}{2} \end{gathered}$$

(iv) $4\sqrt{12}-\sqrt{75}-7\sqrt{48}$

$$\begin{gathered} =4\sqrt{4\times 3}-\sqrt{25\times 3}-7\sqrt{16\times 3} \\ =8\sqrt{3}-5\sqrt{3}-28\sqrt{3} \\ =-25\sqrt{3} \end{gathered}$$

(v) $2\sqrt{48}-\sqrt{75}-\frac{1}{\sqrt{3}}$

$$\begin{gathered} =2\sqrt{16\times 3}-\sqrt{25\times 3}-\frac{1}{\sqrt{3}}\times \frac{\sqrt{3}}{\sqrt{3}} \\ =8\sqrt{3}-5\sqrt{3}-\frac{\sqrt{3}}{3} \\ =3\sqrt{3}-\frac{\sqrt{3}}{3} \\ =\frac{9\sqrt{3}-\sqrt{3}}{3} \\ =\frac{8\sqrt{3}}{3} \end{gathered}$$