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Simplify : 0.06254+0.0083+0.09−162⋅5×3253\dfrac{\sqrt[4]{0.0625}+\sqrt[3]{0.008}+\sqrt{0.09}-1}{\sqrt[3]{62 \cdot 5 \times \sqrt[5]{32}}}

Solution

✅ Correct Option: 3

Let's simplify the numerator first:

0.06254=1164=12\sqrt[4]{0.0625} = \sqrt[4]{\frac{1}{16}} = \frac{1}{2} (since (12)4=116(\frac{1}{2})^4 = \frac{1}{16})

0.0083=810003=15\sqrt[3]{0.008} = \sqrt[3]{\frac{8}{1000}} = \frac{1}{5} (since (15)3=1125(\frac{1}{5})^3 = \frac{1}{125})

0.09=9100=310\sqrt{0.09} = \sqrt{\frac{9}{100}} = \frac{3}{10}

So numerator =12+15+310−1=\frac{1}{2} + \frac{1}{5} + \frac{3}{10} - 1

Converting to common denominator in numerator:

510+210+310−1010\frac{5}{10} + \frac{2}{10} + \frac{3}{10} - \frac{10}{10}

=10−1010= \frac{10-10}{10}

=0= 0

Therefore, entire expression =062.53×325=0=\frac{0}{\sqrt[3]{62.5} × \sqrt[5]{32}}= 0

The answer is 00.

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