Question
Simplify : $\frac{\sqrt{18}}{5 \sqrt{18}+3 \sqrt{72}-2 \sqrt{162}}$
✓
Answer
$ \frac{\sqrt{18}}{5 \sqrt{18}+3 \sqrt{72}-2 \sqrt{162}}$
$ =\frac{\sqrt{9 \times 2}}{5 \sqrt{9 \times 2}+3 \sqrt{36 \times 2}-2 \sqrt{81 \times 2}}$
$ =\frac{3 \sqrt{2}}{15 \sqrt{2}+18 \sqrt{2}-18 \sqrt{2}}$
$ =\frac{3 \sqrt{2}}{15 \sqrt{2}}$
$ =\frac{1}{5}$
$ =\frac{\sqrt{9 \times 2}}{5 \sqrt{9 \times 2}+3 \sqrt{36 \times 2}-2 \sqrt{81 \times 2}}$
$ =\frac{3 \sqrt{2}}{15 \sqrt{2}+18 \sqrt{2}-18 \sqrt{2}}$
$ =\frac{3 \sqrt{2}}{15 \sqrt{2}}$
$ =\frac{1}{5}$
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