Toán Lớp 9: √11+2√18 √14-6√5 √17-12√2 √27-12√5 √28-12√5 √7-3√5 √4+ √15

Question

Toán Lớp 9:  √11+2√18  √14-6√5  √17-12√2  √27-12√5  √28-12√5  √7-3√5  √4+ √15

lanminhngoc · Answer

Giải đáp+Lời giải và giải thích chi tiết:   sqrt{11+2sqrt{18}}   =sqrt{9+2sqrt(9.2)+2}   =sqrt{(3+sqrt2)^2}   =3+sqrt2   sqrt{14-6sqrt5}   =sqrt{9-2.3.sqrt5+5}   =sqrt{(3-sqrt5)^2}   =3-sqrt5   sqrt{17-12sqrt2}   =sqrt{9-2.3.2sqrt+8}   =sqrt{(3-2sqrt2)^2}   =3-2sqrt2   sqrt{27-12sqrt5}   =sqrt{3(9-4sqrt5)}   =sqrt{3(5-2.2.sqrt5+4)}   =sqrt{3(sqrt5-2)^2}   =sqrt3(sqrt5-2)   =sqrt{15}-2sqrt3   sqrt{28-12sqrt5}   =sqrt{2(14-6sqrt5)}   =sqrt{2(9-2.3.sqrt5+5)}   =sqrt{2(3-sqrt5)^2}   =sqrt2(3-sqrt5)   =3sqrt2-sqrt(10)   sqrt{7-3sqrt5}   =sqrt{(14-6sqrt5).2}   =sqrt{1/22(9-2.3.sqrt5+5)}   =sqrt{1/2(3-sqrt5)^2}   =(3-sqrt5)/sqrt2   =(3sqrt2-sqrt(10))/2   sqrt{4+sqrt{15}}   =sqrt{(8+2sqrt(15))/2}   =sqrt{(5+2sqrt{5.3}+3)/2}   =sqrt{(sqrt5+sqrt3)^2/2}   =(sqrt5+sqrt3)/sqrt2   =sqrt{10}+sqrt6