Question

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$( sqrt{2-1} ) sqrt{4+ sqrt{9-4 sqrt{2} } }$

Answer 1

$( sqrt{2} -1) sqrt{4+ sqrt{9-4sqrt{2}} } =(sqrt{2}-1) sqrt{4+ sqrt{(2sqrt{2}-1)^2} } = \ =(sqrt{2}-1) sqrt{3+2sqrt{2}} =(sqrt{2}-1) sqrt{(sqrt{2}+1)^2} =(sqrt{2}-1)(sqrt{2}+1)=2-1=1$