Question

Номер 783 помогите пж

Answer 1

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

$(2 sqrt{2} -1)^2=(2 sqrt{2})^2+1^2-2*2 sqrt{2} *1=8+1-4 sqrt{2} =9-4 sqrt{2}$
$(sqrt{2} +1)^2=(sqrt{2})^2+1^2+2* sqrt{2} *1=2+1+2 sqrt{2} =3+2 sqrt{2}$
2)
$sqrt{49-12 sqrt{5} } * sqrt{49+12 sqrt{5} }= sqrt{(49-12 sqrt{5})(49+12 sqrt{5})} =$$sqrt{49^2-(12 sqrt{5})^2 }= sqrt{2401-720}= sqrt{1681}=41$