Question
Simplify:
$\frac{\sqrt{0.2304}\ +\sqrt{0.1764}}{\sqrt{0.2304}\ -\sqrt{0.1764}}$
$\frac{\sqrt{0.2304}\ +\sqrt{0.1764}}{\sqrt{0.2304}\ -\sqrt{0.1764}}$
✓
Answer
We have,
$\sqrt{0.2304}=\sqrt{\frac{2304}{10000}}$
$=\frac{\sqrt{2\times2\times2\times2\times2\times2\times3\times3}}{\sqrt{10000}}$
$\frac{2\times2\times2\times2\times3}{100}$
$=0.48$
$\sqrt{0.1764}=\sqrt{\frac{1764}{10000}}$
$=\frac{\sqrt{2\times2\times3\times3\times7\times7}}{\sqrt{10000}}$
$=\frac{2\times3\times7}{100}$
$=0.42$
$\frac{\sqrt{0.2304}\ +\sqrt{0.1764}}{\sqrt{0.2304}\ -\sqrt{0.1764}}=\frac{0.48+0.42}{0.48-0.42}$
$=\frac{0.9}{0.06}$
$=15$
$\sqrt{0.2304}=\sqrt{\frac{2304}{10000}}$
$=\frac{\sqrt{2\times2\times2\times2\times2\times2\times3\times3}}{\sqrt{10000}}$
$\frac{2\times2\times2\times2\times3}{100}$
$=0.48$
$\sqrt{0.1764}=\sqrt{\frac{1764}{10000}}$
$=\frac{\sqrt{2\times2\times3\times3\times7\times7}}{\sqrt{10000}}$
$=\frac{2\times3\times7}{100}$
$=0.42$
$\frac{\sqrt{0.2304}\ +\sqrt{0.1764}}{\sqrt{0.2304}\ -\sqrt{0.1764}}=\frac{0.48+0.42}{0.48-0.42}$
$=\frac{0.9}{0.06}$
$=15$
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