Question

√(3+√(5-√(13+√48)))+√(1-√(5-√(13+√48)))=

Answer 1

$sqrt{3+ sqrt{5- sqrt{13+ sqrt{48} } } } + sqrt{1- sqrt{5- sqrt{13+ sqrt{48} } } } =\ \ \ = sqrt{3+ sqrt{5- sqrt{( sqrt{12}+1)^2 } } } + sqrt{1- sqrt{5- sqrt{( sqrt{12}+1)^2 } } } =\ \ \ = sqrt{3+ sqrt{5- sqrt{12}-1 } } + sqrt{1- sqrt{5- sqrt{12}-1 } } =\ \ \ = sqrt{3+ sqrt{4- sqrt{12} } } + sqrt{1- sqrt{4- sqrt{12} } } =\ \ \ = sqrt{3+ sqrt{ (sqrt{3}-1)^2 } } + sqrt{1-( sqrt{3}-1)^2 } =\ \ \ = sqrt{3+ sqrt{3}-1 } + sqrt{1-sqrt{3}+1} =$$=sqrt{2+sqrt{3}}+sqrt{2-sqrt{3}}=sqrt{(sqrt{1.5}+sqrt{0.5})^2}+sqrt{(sqrt{1.5}-sqrt{0.5})^2}=\ \ \ =|sqrt{1.5}+sqrt{0.5}|+|sqrt{1.5}-sqrt{0.5}|=sqrt{1.5}+sqrt{0.5}+sqrt{1.5}-sqrt{0.5}= sqrt{6}$