JIPMAT 2024 (QA) - Simplify : [4]0.0625+[3]0.008+sqrt(0.09)-1[3]62 * 5 x [5]32 | PYQs + Solutions

JIPMAT 2024

Algebra

Indices

Medium

Simplify : $\dfrac{\sqrt[4]{0.0625}+\sqrt[3]{0.008}+\sqrt{0.09}-1}{\sqrt[3]{62 \cdot 5 \times \sqrt[5]{32}}}$

1.25

\frac{1}{5}

Correct Option: 3

1) Let's simplify the numerator first:

\newline

\sqrt[4]{0.0625} = \sqrt[4]{\frac{1}{16}} = \frac{1}{2}

(since

(\frac{1}{2})^4 = \frac{1}{16}

)

\sqrt[3]{0.008} = \sqrt[3]{\frac{8}{1000}} = \frac{1}{5}

(since

(\frac{1}{5})^3 = \frac{1}{125}

)

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

So numerator =

\frac{1}{2} + \frac{1}{5} + \frac{3}{10} - 1

2) Converting to common denominator in numerator:

\frac{5}{10} + \frac{2}{10} + \frac{3}{10} - \frac{10}{10}

= \frac{10-10}{10}

= 0

3) Therefore, entire expression =

\frac{0}{\sqrt[3]{62.5} × \sqrt[5]{32}}

\newline

= 0

The answer is

0