Lời giải:
Ta có: \(\sqrt{10+2\sqrt{6}-2\sqrt{10}-2\sqrt{15}}=\sqrt{5+(5+2\sqrt{6})-(2\sqrt{10}+2\sqrt{15})}\)
\(=\sqrt{5+(2+3+2\sqrt{2.3})-2\sqrt{5}(\sqrt{2}+\sqrt{3})}\)
\(=\sqrt{5+(\sqrt{2}+\sqrt{3})^2-2.\sqrt{5}.(\sqrt{2}+\sqrt{3})}\)
\(=\sqrt{[\sqrt{5}-(\sqrt{2}+\sqrt{3})]^2}=|\sqrt{5}-(\sqrt{2}+\sqrt{3})|=\sqrt{2}+\sqrt{3}-\sqrt{5}\)
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: \(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)
1.\(\sqrt{10+2\sqrt{6}+2\sqrt{10}+2\sqrt{15}}\)
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
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)(\(20\sqrt{300}-15\sqrt{675}+5\sqrt{75}\)):\(\sqrt{15}\)
Rút gọn\(B=\frac{3\sqrt{8}+2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\\ C=\left(4+\sqrt{15}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
So sánh
\(3+\sqrt{5}và2\sqrt{2}+\sqrt{6}\\ 2\sqrt{3}+4và3\sqrt{2}+\sqrt{10}\\ 18và\sqrt{15}\cdot\sqrt{17}\)
Thực hiện phép tính
a) \(\left(4+\sqrt{5}\right)\left(\sqrt{10}-\sqrt{6}\right)\sqrt{4-\sqrt{15}}\)
b) \(\sqrt{3-\sqrt{5}}\left(\sqrt{10}-\sqrt{2}\right)\left(3+\sqrt{5}\right)\)
c) \(\frac{\sqrt{\sqrt{5+2}}+\sqrt{\sqrt{5}-2}}{\sqrt{\sqrt{5}+2}}-\sqrt{3-2\sqrt{2}}\)