Question

упростите выражение
$sqrt{7-2 sqrt{6} } + sqrt{7+2 sqrt{6} }$

Answer 1

$sqrt{7-2 sqrt{6} } + sqrt{7+2 sqrt{6} } = \ = sqrt{( sqrt{6})^2 -2cdot sqrt{6}cdot1+1^2 } + sqrt{( sqrt{6})^2 +2cdot sqrt{6}cdot1+1^2} = \ = sqrt{( sqrt{6}-1)^2} + sqrt{( sqrt{6}+1)^2} =| sqrt{6}-1| + | sqrt{6}+1|= \ = sqrt{6}-1 + sqrt{6}+1=2 sqrt{6}$