Question

which is greter among √12-√11 and √11_√10​

Answer 1

Answer:

$\sqrt{12} - \sqrt{11} \times \frac{ \sqrt{12} + \sqrt{11} }{ \sqrt{12} + \sqrt{11} } \\ \frac{ \sqrt{ {12}^{2} } - \sqrt{ {11}^{2} } }{ \sqrt{12} + \sqrt{11} } \\ \frac{1}{ \sqrt{12} + \sqrt{11} } = = = = = = = 1$

$\sqrt{11} - \sqrt{10} \\ \sqrt{11} - \sqrt{10} \times \frac{ \sqrt{11} + \sqrt{10} }{ \sqrt{11} + \sqrt{10} } \\ \frac{ { \sqrt{11} }^{2} - { \sqrt{10} }^{2} }{ \sqrt{11} + \sqrt{10} } \\ \frac{1}{ \sqrt{11} + \sqrt{10} } = = = = = = 2$

on comparing eq 1 and 2

$\frac{1}{ \sqrt{11} + \sqrt{10} } \: is \: greater \: than \frac{1}{ \sqrt{11} + \sqrt{12} }$

so

$\sqrt{11} - \sqrt{10} \: is \: greater \: than \: \sqrt{12} - \sqrt{11}$

hope it helps.......