Question

Упростите выражения:

Answer 1

1) $sqrt{sqrt{28-16sqrt3}}=sqrt{sqrt{12-2*2sqrt3*4+16}}=sqrt{|2sqrt3-4|}=[2sqrt3=sqrt{12}<sqrt{16}=4]=sqrt{4-2sqrt3}=sqrt{3-2sqrt3+1}=sqrt3-1$

2) $sqrt{2+sqrt{2+sqrt{2+sqrt3}}}sqrt{2-sqrt{2+sqrt{2+sqrt3}}}=sqrt{(2+sqrt{2+sqrt{2+sqrt3}})(2-sqrt{2+sqrt{2+sqrt3}})}=sqrt{4-(2+sqrt{2+sqrt3})}=sqrt{2-sqrt{2+sqrt3}}$$sqrt{2+sqrt3}sqrt{2+sqrt{2+sqrt3}}sqrt{2+sqrt{2+sqrt{2+sqrt3}}}sqrt{2-sqrt{2+sqrt{2+sqrt3}}}=\ sqrt{2+sqrt3}sqrt{2+sqrt{2+sqrt3}}sqrt{2-sqrt{2+sqrt3}}=sqrt{2+sqrt3}sqrt{(2+sqrt{2+sqrt3})(2-sqrt{2+sqrt3})}=sqrt{2+sqrt3}sqrt{(4-(2+sqrt3)}=sqrt{2+sqrt3}sqrt{2-sqrt3}=sqrt{4-3}=1$