Question

which is greater √6-√5 or √11-√10​

Answer 1

Answer:

$\sqrt{6 } - \sqrt{5}$

is greater

Answer 2

${( \sqrt{6} - \sqrt{5}) }^{2} = 6 + - 2 \sqrt{30 } + 5 \\ = 11 - 2 \sqrt{30} .....1 \\ \\ {( \sqrt{11} - \sqrt{10}) }^{2} = 11 - 2 \sqrt{110} + 10 \\ = 21 - 2 \sqrt{110}.........2$

we observe that

from equation 1 and 2

$21 - 2 \sqrt{110} > 11 - \sqrt{30} \\ \\ therefore \\ \sqrt{11} - \sqrt{10} > \sqrt{6} - \sqrt{5}$