Question

Find the value of 54250−−−√3 (a) 925 (b) 35 (c) 27125 (d) 2√35​

Answer 1

$\displaystyle \sf{ \sqrt[3]{ \frac{54}{250} } = \frac{3}{5} }$

Given : $\displaystyle \sf{ \sqrt[3]{ \frac{54}{250} } }$

To find : The value is

$\displaystyle \sf{ (A) \: \: \frac{9}{25} }$

$\displaystyle \sf{ (B) \: \: \frac{3}{5} }$

$\displaystyle \sf{ (C) \: \: \frac{27}{125} }$

$\displaystyle \sf{ (D) \: \: \frac{ \sqrt[3]{2} }{5} }$

Solution :

Here the given expression is

$\displaystyle \sf{ \sqrt[3]{ \frac{54}{250} } }$

We simplify it as below

$\displaystyle \sf{ \sqrt[3]{ \frac{54}{250} } }$

$\displaystyle \sf{ = \sqrt[3]{ \frac{2 \times 3 \times 3 \times 3}{5 \times 5 \times 5 \times 2} } }$

$\displaystyle \sf{ = \sqrt[3]{ \frac{ 3 \times 3 \times 3}{5 \times 5 \times 5 } } }$

$\displaystyle \sf{ = \sqrt[3]{ \frac{ {3}^{3} }{ {5}^{3} } } }$

$\displaystyle \sf{ = \frac{3}{5} }$

Hence the correct option is $\displaystyle \sf{ (B) \: \: \frac{3}{5} }$

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