Question

plz answer this question plzzzzz
The question is
compare the following pairs of ratio​

Answer 1

$\fbox \red { √15/√8 is greater }$

First of all

all we need to do is to rationalise each of the terms.

Let's rationalise the 1st one

$\frac{ \sqrt{15} }{ \sqrt{8} } \\ \frac{ \sqrt{15} }{ \sqrt{8} } \times \frac{ \sqrt{8} }{ \sqrt{8} } \\ \\ \frac{ \sqrt{120} }{ \sqrt{64} } \\ \\ \frac{ \sqrt{120} }{8} .......(eq \: 1)$

Now rationalise the 2nd term.

$\frac{ \sqrt{8} }{ \sqrt{15} } \\ \\ \frac{ \sqrt{8} }{ \sqrt{15} } \times \frac{ \sqrt{15} }{ \sqrt{15} } \\ \\ \frac{ \sqrt{120} }{ \sqrt{225} } \\ \\ \frac{ \sqrt{120} }{15} ....... \: (eq \: 2)$

Comparing equation 1 & 2 by cross - multiplication

$\frac{ \sqrt{120} }{8} : \: \frac{ \sqrt{120} }{15} \\ \\ \sqrt{120} \times 15 \: : \: \sqrt{120} \times 8 \\ \\ 15 \sqrt{120} \: : \: 8 \sqrt{120}$

Hence 15√120 is greater than 8√120

Therefore the first term is greater

that is √15/√8 > √8/√15