\(\sqrt{12-2\sqrt{35}}=?\)
\(\sqrt{4+\sqrt{15}}=?\)
\(\left(3-\sqrt{2}\right)\sqrt{11+6\sqrt{2}}=?\)
\(\left(\sqrt{5}+\sqrt{7}\right)\sqrt{12-2\sqrt{35}=?}\)
\(\sqrt{7-2\sqrt{10}-\sqrt{7+2\sqrt{10}}=?}\)
\(\sqrt{13-\sqrt{160}+\sqrt{53+4\sqrt{90}}}\)
giúp mình với ạ !! thks trước. đề của mấy bài này là tính ạ
a) \(\sqrt{12-2\sqrt{35}}=\sqrt{\left(\sqrt{5}-\sqrt{7}\right)^2}=\sqrt{7}-\sqrt{5}\)
b) \(\sqrt{4+\sqrt{15}}=...\)
c) \(\left(3-\sqrt{2}\right)\sqrt{11+6\sqrt{2}}=\left(3\sqrt{2}\right)\sqrt{\left(3+\sqrt{2}\right)^2}\\ =\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)=9-2=7\)
d) \(\left(\sqrt{5}+\sqrt{7}\right)\sqrt{12-2\sqrt{35}}=\left(\sqrt{7}+\sqrt{5}\right)\sqrt{\left(\sqrt{5}-\sqrt{7}\right)^2}\\ =\left(\sqrt{7}+\sqrt{5}\right)\left(\sqrt{7}-\sqrt{5}\right)=7-5=2\)
e) \(\sqrt{7-2\sqrt{10}-\sqrt{7+2\sqrt{10}}}=\sqrt{7-2\sqrt{10}-\sqrt{\left(\sqrt{2}+\sqrt{5}\right)^2}}\\ =\sqrt{7-2\sqrt{10}-\left(\sqrt{2}+\sqrt{5}\right)}=\sqrt{7-2\sqrt{10}-\sqrt{2}-\sqrt{5}}\\ =\sqrt{7-2\sqrt{10}-\sqrt{2}-\sqrt{5}}\)
f) \(\sqrt{13-\sqrt{160}+\sqrt{53}+4\sqrt{90}}=\sqrt{13-4\sqrt{10}+\sqrt{53}+12\sqrt{10}}\\ =\sqrt{13+8\sqrt{10}+\sqrt{53}}\)