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Proportion

Simplify: √3...

Question

Simplify:
$\sqrt{\frac{3 a}{2} (\frac{3 a}{2}) (\frac{3 a}{2} - a) (\frac{3 a}{2} - a)}$

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Solution

$\sqrt{\frac{3 a}{2} (\frac{3 a}{2}) (\frac{3 a}{2} - a) (\frac{3 a}{2} - a)}$
$= \sqrt{{(\frac{3 a}{2})}^{2} {(\frac{3 a}{2} - a)}^{2}}$
$= (\frac{3 a}{2}) (\frac{3 a}{2} - a)$
$= (\frac{3 a}{2}) (\frac{a}{2})$
$= (\frac{3 a^{2}}{4})$

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