ÁP dụng hđt (a+b+c)2 =a2 +b2 +c2 +2ab+2ac+2bc
\(\Rightarrow\) \(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}=\sqrt{2+3+5+2\sqrt{2}\times\sqrt{3}+2\sqrt{2}\times\sqrt{5}+2\sqrt{3}\times\sqrt{5}}=\sqrt{\left(\sqrt{2}+\sqrt{3}+\sqrt{5}\right)^2}=\left|\sqrt{2}+\sqrt{3}+\sqrt{5}\right|=\sqrt{2}+\sqrt{3}+\sqrt{5}\)
1)\(\sqrt{4+\sqrt{10+2\sqrt{5}}}+\sqrt{4-\sqrt{10+2\sqrt{5}}}\)
2)\(\sqrt{35+12\sqrt{6}}-\sqrt{35-12\sqrt{6}}\)
3)\(\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
\(\sqrt{10+2\sqrt{6}-2\sqrt{10}-2\sqrt{15}}\)
Tính: \(\sqrt{10+2\sqrt{6}-2\sqrt{10}-2\sqrt{15}}\)
Tính: \(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)
a,\(\sqrt{1+2\sqrt{2}+\sqrt{11+6\sqrt{2}}}\)
b,\(\sqrt{10-2\sqrt{21}}+\sqrt{4+2\sqrt{3}}\)
c,\(\sqrt{1+\dfrac{\sqrt{3}}{2}}+\sqrt{1-\dfrac{\sqrt{3}}{2}}\)
d,\(\sqrt{15+6\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)
Rút gọn
a)\(\sqrt{4-2\sqrt{ }3}-\sqrt{3}\)
b)\(\sqrt{11+6\sqrt{ }2}-3+\sqrt{2}\)
c)\(\sqrt{7+2\sqrt{ }10}-\sqrt{7-2\sqrt{ }10}\)
d)(\(20\sqrt{300}-15\sqrt{675}+5\sqrt{75}\)):\(\sqrt{15}\)
bài 1 Tính giá trị biểu thức:
a)\(\sqrt{1,44}+3\sqrt{1,69}\)
b)\(\sqrt{0,04}+2\sqrt{0,25}\)
bài 2 bài 2 so sánh
a) 2\(\sqrt{31}\) và 10
b) \(\sqrt{15}-1\) và \(\sqrt{10}\)
Rút gọn\(B=\frac{3\sqrt{8}+2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\\ C=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
1.\(\sqrt{\frac{129}{16}+\sqrt{2}}\)
2.\(\sqrt{\frac{289+4\sqrt{72}}{16}}\)
3. \(\sqrt{2-\sqrt{3}}.\left(\sqrt{6}+\sqrt{2}\right)\)
4.\(\left(\sqrt{21}+7\right).\sqrt{10-2\sqrt{21}}\)
5.\(2.\left(\sqrt{10}-\sqrt{2}\right).\sqrt{4+\sqrt{6-2\sqrt{5}}}\)
6.\(\left(4\sqrt{2}+\sqrt{30}\right).\left(\sqrt{5}-\sqrt{3}\right).\sqrt{4-\sqrt{15}}\)
7.\(\left(7+\sqrt{14}\right).\sqrt{9-2\sqrt{14}}\)
