Question
Simplify the following:
$\frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9}$
$\frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9}$
✓
Answer
$\frac{\sqrt{24}}{8}+\frac{\sqrt{54}}{9}=\frac{\sqrt{4\times5}}{8}+\frac{\sqrt{9\times6}}{9}$
$\frac{2\sqrt{6}}{8}+\frac{3\sqrt{6}}{9}=\frac{\sqrt{6}}{4}+\frac{\sqrt{6}}{3}$
$=\sqrt{6}\Big(\frac{1}{4}+\frac{1}{3}\Big)$
$=\sqrt{6}\Big(\frac{3+4}{12}\Big)=\frac{7\sqrt{6}}{12}$
$\frac{2\sqrt{6}}{8}+\frac{3\sqrt{6}}{9}=\frac{\sqrt{6}}{4}+\frac{\sqrt{6}}{3}$
$=\sqrt{6}\Big(\frac{1}{4}+\frac{1}{3}\Big)$
$=\sqrt{6}\Big(\frac{3+4}{12}\Big)=\frac{7\sqrt{6}}{12}$
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