Question
Very-Short-Answer Questions:
Simplify: $\frac{\big(2\sqrt{45}+3\sqrt{20}\big)}{2\sqrt{5}}$
Simplify: $\frac{\big(2\sqrt{45}+3\sqrt{20}\big)}{2\sqrt{5}}$
✓
Answer
$\frac{\big(2\sqrt{45}+3\sqrt{20}\big)}{2\sqrt{5}}$
$=\frac{\big(2\sqrt{45}+3\sqrt{20}\big)}{2\sqrt{5}}\times\frac{2\sqrt5}{2\sqrt5}$ ...(Rationlising the denominator)
$=\frac{2\sqrt5\big(2\sqrt{45}+3\sqrt{20}\big)}{20}$
$=\frac{4\sqrt{45\times5}+6\sqrt{20\times5}}{20}$
$=\frac{4\sqrt{3^2\times5^2}+6\sqrt{2^2\times5^2}}{20}$
$=\frac{4(3\times5)+6(2\times5)}{20}$
$=\frac{60+60}{20}$
$=6$
$=\frac{\big(2\sqrt{45}+3\sqrt{20}\big)}{2\sqrt{5}}\times\frac{2\sqrt5}{2\sqrt5}$ ...(Rationlising the denominator)
$=\frac{2\sqrt5\big(2\sqrt{45}+3\sqrt{20}\big)}{20}$
$=\frac{4\sqrt{45\times5}+6\sqrt{20\times5}}{20}$
$=\frac{4\sqrt{3^2\times5^2}+6\sqrt{2^2\times5^2}}{20}$
$=\frac{4(3\times5)+6(2\times5)}{20}$
$=\frac{60+60}{20}$
$=6$
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