Question

compare the ratios √13 /√8 , √8 /√5
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Answer 1

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

TO COMPARE

$\displaystyle \sf{ \frac{ \sqrt{13} }{ \sqrt{8} } \: \: \: \: \: and \: \: \: \: \frac{ \sqrt{8} }{ \sqrt{5} } \: }$

CALCULATION

$\sf{The \: denominators \: of \: the \: ratios \: are \: \: \sqrt{8} \: \: and \: \: \sqrt{5} }$

Now LCM of 8 & 5 = 40

We rewrite the given ratios as follows

$\displaystyle \sf{ \frac{ \sqrt{13} }{ \sqrt{8} } = \frac{ \sqrt{13 \times 5} }{ \sqrt{8 \times 5} } = \frac{ \sqrt{65} }{ \sqrt{40} } \: }$

$\displaystyle \sf{ \frac{ \sqrt{8} }{ \sqrt{5} } = \frac{ \sqrt{8 \times 8} }{ \sqrt{8 \times 5} } = \frac{ \sqrt{64} }{ \sqrt{40} } \: }$

$\sf{Since \: \:65 > 64 }$

Hence

$\displaystyle \sf{ \frac{ \sqrt{13} }{ \sqrt{8} } \: \: > \: \: \frac{ \sqrt{8} }{ \sqrt{5} } \: }$

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