Question

Найти значение выражения
$(3-sqrt{2}) sqrt{17+6 sqrt{4- sqrt{9+4 sqrt{2} } } }$

Answer 1

$(3- sqrt{2}) sqrt{17+ 6 sqrt{4- sqrt{9+4 sqrt{2} } } } = \ = sqrt{(3- sqrt{2})^2( 17+ 6 sqrt{4- sqrt{(1+2 sqrt{2})^2 } })}}= \ = sqrt{(11-6 sqrt{2})(17+ 6 sqrt{3-2 sqrt{2} } )} } = \ = sqrt{(11-6 sqrt{2})(17+6 sqrt{( sqrt{2}-1)^2 }) } = \ = sqrt{(11-6 sqrt{2})(11+6 sqrt{2}) }= \ = sqrt{121-72}= sqrt{49}=7$