Question

what is the value of root 162 + root 108 divided by root 72 + root 48

Answer 1

Dear student,
Here is the solution of your asked query:
$$\begin{gathered} \frac{\sqrt{162}+\sqrt{108}}{\sqrt{72}+\sqrt{48}} \\ =\frac{\sqrt{9\times 9\times 2}{\displaystyle +}{\displaystyle \sqrt{6\times 6\times 3}}}{\sqrt{6\times 6\times 2}{\displaystyle +}{\displaystyle \sqrt{4\times 4\times 3}}} \\ =\frac{9\sqrt{2}+6\sqrt{3}}{6\sqrt{2}+4\sqrt{3}} \\ =\frac{{\displaystyle 9\sqrt{2}+6\sqrt{3}}}{{\displaystyle 6\sqrt{2}+4\sqrt{3}}}\times \frac{{\displaystyle 6\sqrt{2}-4\sqrt{3}}}{{\displaystyle 6\sqrt{2}-4\sqrt{3}}} \\ =\frac{9\sqrt{2}\left(6\sqrt{2}-4\sqrt{3}\right)+6\sqrt{3}\left(6\sqrt{2}-4\sqrt{3}\right)}{{\displaystyle {\left(6\sqrt{2}\right)}^2}{\displaystyle -}{\displaystyle {{\displaystyle \left(4\sqrt{3}\right)}}^2}} \\ =\frac{108-36\sqrt{6}+36\sqrt{6}-72}{72-48} \\ =\frac{36}{24}=\frac{3}{2} \end{gathered}$$
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