Question

a44 решите пожалуйста

Answer 1

$sqrt{22 - sqrt{160} } ( sqrt{10} + 1) = \ = sqrt{22 - 4 sqrt{10} } ( sqrt{10} + 1) = \ = sqrt{2(11 - 2 sqrt{10} )} ( sqrt{10} + 1) = \ = sqrt{2} cdot sqrt{( ({ sqrt{10}) }^{2} - 2 sqrt{10} + 1) } ( sqrt{10} + 1) = \ = sqrt{2} cdot sqrt{( sqrt{10} - 1) ^{2} } ( sqrt{10} + 1) = \ = sqrt{2} cdot | sqrt{10} - 1 | ( sqrt{10} + 1) = \ = sqrt{2} cdot ( sqrt{10} - 1 ) ( sqrt{10} + 1) = \ = ( {( sqrt{10} )}^{2} - {1}^{2}) sqrt{2} = \ = (10 - 1) sqrt{2} = 9 sqrt{2}$