The correct option is A 35 √(54250) #160; ⇒ #160; √(27 × 2125 × 2) #160; ⇒ √(3^35^3) ⇒35 ...

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Inverse of a Function

√54250 equals...

Question

$\sqrt[3]{\frac{54}{250}}$ equals :

\frac{9}{25}

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\frac{3}{5}

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\frac{27}{125}

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\frac{\sqrt[3]{2}}{5}

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Solution

$\sqrt[3]{\frac{54}{250}}$
$= \sqrt[3]{\frac{27 \times 2}{125 \times 2}}$
$= \sqrt[3]{\frac{3^{3}}{5^{3}}}$
$= \sqrt[3]{(\frac{3}{5})^{3}}$ [Since, $\frac{a^{m}}{b^{m}} = (\frac{a}{b})^{m}, b \neq 0$ ]
$= {(\frac{3}{5})^{3}}^{\frac{1}{3}}$ [Since, $\sqrt[n]{x} = x^{\frac{1}{n}}$ ]
$= \frac{3}{5}$ [Since, $(a^{m})^{n} = a^{m n}$ ]
$∴, \sqrt[3]{\frac{54}{250}} = \frac{3}{5}$
Hence, Option A is correct.

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