Bài 1:Thực hiện phép tính
1. \(\sqrt{27}-3\sqrt{48}-2\sqrt{75}-\sqrt{\left(2-\sqrt{3}\right)^2}\)
2.\(\left(\sqrt{8}-5\sqrt{2}+\sqrt{20}\right).\sqrt{5}+\left(40\sqrt{\frac{1}{10}}-10\right)\)
3.\(\left(\sqrt{24}-\sqrt{\frac{2}{3}}-\sqrt{\frac{1}{6}}+\sqrt{\frac{3}{2}}\right).\sqrt{6}\)
Thực hiện phép tính:
\(\frac{6}{2-\sqrt{10}}-\frac{2\sqrt{5}-5\sqrt{2}}{\sqrt{2}-\sqrt{5}}+\sqrt{41+4\sqrt{10}}\)
Bài 3: Thực hiện phép tính
1) \(2\sqrt{5}-\sqrt{125}-\sqrt{80}+\sqrt{605}\)
2) \(\frac{10-2\sqrt{10}}{\sqrt{5}+\sqrt{2}}+\frac{8}{1-\sqrt{5}}\)
3)\(\sqrt{15-\sqrt{216}}+\sqrt{33-12\sqrt{6}}\)
5)\(\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}}+\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}\)
6)\(6\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\)
7)\(2\sqrt{27}-6\sqrt{\frac{4}{3}}+\frac{3}{5}\sqrt{75}\)
8)\(\frac{\sqrt{3-\sqrt{5}}.\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
9)\(\sqrt{2-\sqrt{3}}\left(\sqrt{5}+\sqrt{2}\right)\)
THỰC HIỆN PHÉP TÍNH:
22) \(\frac{1}{\sqrt{5}+\sqrt{2}}+\frac{1}{\sqrt{5}-\sqrt{2}}\)
23) \(\frac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\frac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)
24) \(\frac{\sqrt{18}}{\sqrt{2}}-\frac{\sqrt{12}}{\sqrt{3}}\)
25) \(\sqrt{\left(\sqrt{5}+1\right)^2}+\sqrt{\left(\sqrt{5}-1\right)^2}\)
27) \(\sqrt{3-2\sqrt{2}}\)
28) \(\frac{1}{\sqrt{8}+\sqrt{7}}+\sqrt{175}-2\sqrt{2}\)
30) \(\left(2\sqrt{1\frac{9}{16}}-\sqrt{5\frac{1}{16}}\right):\sqrt{16}\)
34) \(\frac{\left(5\sqrt{3}+\sqrt{50}\right)\left(5-\sqrt{24}\right)}{\sqrt{75}-5\sqrt{2}}\)
35) \(\left(2\sqrt{6}-4\sqrt{3}+5\sqrt{2}-\frac{1}{4}\sqrt{8}\right).3\sqrt{6}\)
36) \(\frac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\frac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
39) \(\sqrt{\frac{2-\sqrt{3}}{2+\sqrt{3}}+\sqrt{\frac{2+\sqrt{3}}{2-\sqrt{3}}}}\)
45) \(\frac{\sqrt{6-2\sqrt{5}}}{2-\sqrt{20}}\)
Bài 1: Chứng minh các đẳng thức sau:
a) \(\sqrt{7-2\sqrt{10}}=\sqrt{5}-\sqrt{2}\)
b)\(\sqrt{4+2\sqrt{3}}-\sqrt{3}=1\)
Bài 2: Thực hiện phép tính:
a) \(\frac{4}{\sqrt{3}+1}\frac{1}{\sqrt{3}-2}+\frac{6}{\sqrt{3}-3}\)
b) \(\frac{4}{3+\sqrt{5}}-\frac{8}{1+\sqrt{5}}+\frac{15}{\sqrt{5}}\)
c) \(\frac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}-\frac{5}{\sqrt{6+1}}\)
Thực hiện phép tính
a\(\left(1+\frac{5-\sqrt{5}}{1-\sqrt{5}}\right).\left(\frac{1+\sqrt{5}}{1+\sqrt{5}}+1\right)\) b\(\frac{1}{\sqrt{3}+\sqrt{2}-\sqrt{5}}-\frac{1}{\sqrt{3}+\sqrt{2}+\sqrt{5}}\)
c \(\frac{1}{\sqrt{3}}+\frac{1}{3\sqrt{2}}+\frac{1}{\sqrt{3}}\sqrt{\frac{5}{12}-\frac{1}{\sqrt{6}}}\)
\(\sqrt{50}-3\sqrt{45}-2\sqrt{18}+5\sqrt{20}\)
Thực hiện rút gọn phép tính này nha mng
Thực hiện phép tính:
\(\frac{\sqrt{3}+\sqrt{2}-1}{2+\sqrt{6}}+\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+1}.\left(\frac{\sqrt{3}}{2-\sqrt{6}}+\frac{\sqrt{3}}{2+\sqrt{6}}\right)-\frac{1}{\sqrt{2}}\)
Bài 1:Thực hiện phép tính
1.(\(\sqrt{28}_{ }-\sqrt{12}-\sqrt{7}\))\(\sqrt{7}\)+2\(\sqrt{21}\)
2. 2\(\sqrt{3}\) +\(\sqrt{27}\)-3\(\sqrt{45}\) +\(\sqrt{5}\)
3.(2\(\sqrt{2}\) -\(\sqrt{5}\)+\(\sqrt{18}\)).\(\sqrt{5}+20\sqrt{\frac{1}{10}}\)
4.\(\sqrt{27}-3\sqrt{48}+2\sqrt{75}-\sqrt{\left(2-\sqrt{3}\right)^2}\)
5.(\(\sqrt{8}-5\sqrt{2}+\sqrt{20}\)).\(\sqrt{5}\)+(40\(\sqrt{\frac{1}{10}}-10\)
6. \(\sqrt{2x}-3\sqrt{8x}+4\sqrt{18x}=14\)