Question

Find the square root of 25/2(correct to three decimal places

Answer 1

$\sqrt{ \frac{25}{2} } \\ = \frac{ \sqrt{25} }{ \sqrt{2} } \\ = \frac{5}{ \sqrt{2} } \\ = \frac{5}{1.14} \\ \\ = \frac{500}{114} \\ \\= 4.39 \: (approx.)$

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Answer 2

Take

$y = \sqrt{ \frac{25}{2} }$

Taking log on both sides

$log(y) = log( \sqrt{ \frac{25}{2} } )$

$log( y) = log( { \frac{25}{2} }^{ \frac{1}{2} } )$

$log(y) = \frac{1}{2} log( \frac{25}{2} )$

$log(y) = \frac{1}{2} (log(25) - log(2))$

$log(y) = \frac{(1.39 - 0.30)}{2}$

$log(y) = \frac{1.09}{2}$

$y = antilog(0.54)$

$y = 3.53$

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