Question

Compare the following pair of ratio √13/√8, √7/ √5​

Answer 1

$\displaystyle \sf \frac{ \sqrt{13} }{ \sqrt{8} } \: > \: \frac{ \sqrt{7} }{ \sqrt{5} }$

Given :

$\displaystyle \sf \frac{ \sqrt{13} }{ \sqrt{8} } \:, \: \frac{ \sqrt{7} }{ \sqrt{5} }$

To find :

Compare the ratios

Solution :

Step 1 of 2 :

Write down the given ratios

Here the given ratios are

$\displaystyle \sf \frac{ \sqrt{13} }{ \sqrt{8} } \:, \: \frac{ \sqrt{7} }{ \sqrt{5} }$

Step 2 of 2 :

Compare the given ratios

LCM of 8 and 5 = 40

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

$\displaystyle \sf \frac{ \sqrt{7} }{ \sqrt{5} } = \frac{ \sqrt{7 \times 8} }{ \sqrt{5 \times 8} } = \frac{ \sqrt{56} }{ \sqrt{40} }$

Now ,

$\displaystyle \sf 65 > 56$

$\displaystyle \sf{ \implies } \sqrt{65} > \sqrt{56}$

$\displaystyle \sf{ \implies } \frac{ \sqrt{65} }{ \sqrt{40} } > \frac{ \sqrt{56} }{ \sqrt{40} }$

$\displaystyle \sf{ \implies }\frac{ \sqrt{13} }{ \sqrt{8} } \: > \: \frac{ \sqrt{7} }{ \sqrt{5} }$

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Answer 2

Step-by-step explanation:

कंपेयर रूट 30 अपऑन रूट 8 एंड रूट 7 अपऑन रूट 5