Đặt \(A=\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)
\(\Rightarrow A^2=17+12\sqrt{2}+17-12\sqrt{2}+2\sqrt{\left(17+12\sqrt{2}\right)\left(17-12\sqrt{2}\right)}\)
\(\Rightarrow A^2=34+2\sqrt{289-288}\)
\(\Rightarrow A^2=34+2=36\)
\(\Rightarrow A=\sqrt{36}=6\)
Vậy \(\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}=6\)
rút gọn
\(\sqrt{17+12\sqrt{2}}-\sqrt{17-12\sqrt{2}}\)
\(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
\(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
Rút gọn: \(\sqrt{17-12\sqrt{2}}+\sqrt{17+12\sqrt{2}}\)
Tính \(\frac{\sqrt{3}-2\sqrt{2}}{\sqrt{17}-12\sqrt{2}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
\(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)
\(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}-\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17}-12\sqrt{2}}\)
Tính
giúp mình với ạ
a,\(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)
b,\(\sqrt{31-12\sqrt{3}}-\sqrt{31+12\sqrt{3}}\)
mình cảm ơn nhiều .
\(\sqrt{\left(\sqrt{7}-5\right)^2}+\sqrt{\left(2-\sqrt{7}\right)^2}\)
\(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)
\(\sqrt{17+12\sqrt{2}}+\sqrt{17-12\sqrt{2}}\)
\(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)
