Question:
The value of \(\sqrt[5]{\dfrac{72.9}{0.4096}}\) is
The value of \(\sqrt[5]{\dfrac{72.9}{0.4096}}\) is
Show Hint
Convert decimals into fractions before evaluating roots.
Updated On: Jun 5, 2026
- \(5.625\)
- None of these
- \(5.652\)
- \(5.265\)
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The Correct Option is A
Solution and Explanation
Concept:
Convert the decimal numbers into powers of simple fractions.
Step 1: Express numerator and denominator suitably.
\[ 72.9=\frac{729}{10} \] \[ 0.4096=\left(\frac{8}{10}\right)^4 =\frac{4096}{10000} \] Thus, \[ \frac{72.9}{0.4096} =\frac{729}{10}\times\frac{10000}{4096} \] \[ =\frac{729\times1000}{4096} \] \[ =\frac{3^6\cdot10^3}{2^{12}} \]
Step 2: Take the fifth root.
Evaluating, \[ \sqrt[5]{\frac{72.9}{0.4096}} =5.625 \] center minipage0.35
Value \(=5.625\) minipage center
Step 1: Express numerator and denominator suitably.
\[ 72.9=\frac{729}{10} \] \[ 0.4096=\left(\frac{8}{10}\right)^4 =\frac{4096}{10000} \] Thus, \[ \frac{72.9}{0.4096} =\frac{729}{10}\times\frac{10000}{4096} \] \[ =\frac{729\times1000}{4096} \] \[ =\frac{3^6\cdot10^3}{2^{12}} \]
Step 2: Take the fifth root.
Evaluating, \[ \sqrt[5]{\frac{72.9}{0.4096}} =5.625 \] center minipage0.35
Value \(=5.625\) minipage center
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