Ta có: \(\dfrac{5\sqrt{3}-3\sqrt{5}}{\sqrt{15}}+\dfrac{4}{\sqrt{5}-3}+\dfrac{6}{\sqrt{3}}\)
\(=\dfrac{\sqrt{15}\left(\sqrt{5}-\sqrt{3}\right)}{\sqrt{15}}-\dfrac{4\left(3+\sqrt{5}\right)}{4}+\sqrt{3}\cdot\dfrac{2\sqrt{3}}{\sqrt{3}}\)
\(=\sqrt{5}-\sqrt{3}-3-\sqrt{5}+2\sqrt{3}\)
\(=-3+\sqrt{3}\)
Bài : Thu gọn
1) \(\dfrac{3\sqrt{5}-5\sqrt{3}}{\sqrt{15}-3}\)
2) \(\dfrac{\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{3}}\)
3) \(\dfrac{7+4\sqrt{3}}{2+\sqrt{3}}\)
4) \(\dfrac{16-6\sqrt{7}}{\sqrt{7}-3}\)
5) \(\dfrac{\left(\sqrt{3}-\sqrt{2}\right)^2+4\sqrt{6}}{\sqrt{3}+\sqrt{2}}\)
6) \(\dfrac{\left(\sqrt{3}+2\sqrt{5}\right)^2-8\sqrt{15}}{\sqrt{6-2\sqrt{10}}}\)
Rút gọn:
1) \(\dfrac{3\sqrt{5}-5\sqrt{3}}{\sqrt{15}-3}\)
2) \(\dfrac{\sqrt{5+2\sqrt{6}}}{\sqrt{2}+\sqrt{3}}\)
3) \(\dfrac{7+4\sqrt{3}}{2+\sqrt{3}}\)
Làm mất căn mẫu và thu gọn
1) \(\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}+\dfrac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
2) \(\left(1-\dfrac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\dfrac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)
3) \(\left(\dfrac{3\sqrt{125}}{15}-\dfrac{10-4\sqrt{5}}{\sqrt{5}-2}\right)\dfrac{1}{\sqrt{5}}\)
4) \(\dfrac{1}{1+\sqrt{2}}-\dfrac{1}{1-\sqrt{2}}\)
5) \(\dfrac{1}{3+\sqrt{5}}-\dfrac{1}{\sqrt{5}-3}\)
6) \(\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}\)
7) \(\dfrac{4}{1-\sqrt{3}}+\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\)
8) \(\dfrac{\sqrt{2}-1}{\sqrt{2}+1}-\dfrac{3}{\sqrt{2}-1}\)
9) \(\dfrac{\sqrt{2}}{\sqrt{\sqrt{2}+1}-1}-\dfrac{\sqrt{2}}{\sqrt{\sqrt{2}+1}+1}\)
10) \(\dfrac{\sqrt{15}-\sqrt{12}}{\sqrt{5}-2}-\dfrac{1}{2-\sqrt{3}}\)
11) \(\dfrac{5}{1+\sqrt{6}}-\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}\)
12) \(\dfrac{5}{3-\sqrt{7}}-\dfrac{3}{\sqrt{2}+\sqrt{3}}+\dfrac{-1}{\sqrt{2}-1}\)
Giúp em giải với ạ! Help me~!
5 câu:
1) \(\dfrac{\sqrt{3}+\sqrt{2}}{\sqrt{6}+2}-\dfrac{\sqrt{3}-\sqrt{2}}{\sqrt{6}-2}\)
2) \(\dfrac{3}{\sqrt{5}-\sqrt{2}}-\dfrac{2}{2-\sqrt{2}}+\dfrac{1}{\sqrt{3}+\sqrt{2}}\)
3) \(\dfrac{12}{\sqrt{5}+1}-\dfrac{4}{\sqrt{5}+2}+\dfrac{20}{3+\sqrt{5}}\)
4) \(\dfrac{5}{3-\sqrt{7}}-\dfrac{2}{\sqrt{2}+\sqrt{3}}-\dfrac{1}{\sqrt{2}-1}\)
5) \(\dfrac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\dfrac{3+\sqrt{3}}{\sqrt{3}}-\dfrac{4}{\sqrt{7}-1}\)
tính
1.\(\left(\sqrt{15}-2\sqrt{3}\right)^2+12\sqrt{5}\)
2.\(3\sqrt{2}\left(4-\sqrt{2}\right)+3\left(1-2\sqrt{2}\right)^2\)
3.\(\dfrac{1}{2}\left(\sqrt{6}+\sqrt{5}\right)^2-\dfrac{1}{4}\sqrt{120}-\sqrt{\dfrac{15}{2}}\)
4.\(\left(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}\right)^2\)
5.\(\left(\sqrt{\sqrt{14}+\sqrt{5}}+\sqrt{\sqrt{14}-\sqrt{5}}\right)^2\)
6.\(\left(\sqrt{3}+1\right)^3-\left(\sqrt{3}-1\right)^3\)
7.\(\left(\sqrt{2}+1\right)^3-\left(\sqrt{2}-1\right)^3\)
8.\(\sqrt{13-\sqrt{160}}-\sqrt{53+4\sqrt{90}}\)
9.\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
Rg
a) \(\dfrac{(3\sqrt{3}+\sqrt{50})(5-\sqrt{24})}{\sqrt{75}-5\sqrt{2}}\)
b)\((\dfrac{15}{\sqrt{6}+1}+\dfrac{4}{\sqrt{6}-2}-\dfrac{12}{3-\sqrt{6}})(\sqrt{6}+11)\)
a \(\left(2\sqrt{6-}4\sqrt{3}+5\sqrt{2}-\dfrac{1}{4}\sqrt{8}\right)5\sqrt{6}\)
b \(\left(\dfrac{1}{\sqrt{5-}\sqrt{2}}+\dfrac{1}{\sqrt{5}+\sqrt{2}}+1\right).\dfrac{1}{\sqrt{2}+1^2}\)
c \(\dfrac{3}{\sqrt{2+}\sqrt{7}}\dfrac{1}{\sqrt{2-}\sqrt{7}}-1\)
d \(2x\sqrt{300}-15\sqrt{75}+5\sqrt{75}.15\)
Thực hiện phép tính:
a. \(\left(\dfrac{\sqrt{6}-\sqrt{3}}{5\sqrt{2}-5}+\dfrac{\sqrt{5}}{5}\right):\dfrac{2}{\sqrt{5}-\sqrt{3}}\)
b. \(\dfrac{\sqrt{6}-3}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}\)
tính
1.\(\sqrt{147}+\sqrt{54}-4\sqrt{27}\)
2.\(\sqrt{28}-4\sqrt{63}+7\sqrt{112}\)
3.\(\sqrt{49}-5\sqrt{28}+\dfrac{1}{2}\sqrt{63}\)
4.\(\left(2\sqrt{6}-4\sqrt{3}-\dfrac{1}{4}\sqrt{8}\right).3\sqrt{6}\)
5.(\(2\sqrt{1\dfrac{9}{16}}-5\sqrt{5\dfrac{1}{16}}\)):\(\sqrt{16}\)
6.\(\left(\sqrt{48}-3\sqrt{27}-\sqrt{147}\right):\sqrt{3}\)
7.\(\left(\sqrt{50}-3\sqrt{49}\right):\sqrt{2}-\sqrt{162}:\sqrt{2}\)
8.\(\left(2\sqrt{1\dfrac{9}{10}}-\sqrt{5\dfrac{1}{10}}\right):\sqrt{10}\)
9.\(2\sqrt{\dfrac{16}{3}}-3\sqrt{\dfrac{1}{27}}-6\sqrt{\dfrac{4}{75}}\)
10.\(2\sqrt{27}-6\sqrt{\dfrac{4}{3}}+\dfrac{3}{5}\sqrt{75}\)
11.\(\dfrac{\sqrt{18}}{\sqrt{2}}-\dfrac{\sqrt{12}}{\sqrt{3}}\)
12.\(\dfrac{\sqrt{27}}{\sqrt{3}}+\dfrac{\sqrt{98}}{\sqrt{2}}-\sqrt{175}:\sqrt{7}\)
13.\(\left(\dfrac{\sqrt{8}}{\sqrt{2}}-\dfrac{\sqrt{180}}{\sqrt{5}}\right).\sqrt{5}-\sqrt{\dfrac{81}{11}}.\sqrt{11}\)
14.\(\sqrt{8\sqrt{3}}-2\sqrt{25\sqrt{12}}+4\sqrt{\sqrt{192}}\)
15.\(\left(3\sqrt{2}-2\sqrt{3}\right)\left(3\sqrt{2}+2\sqrt{3}\right)\)
16.\(\left(1+\sqrt{5}-\sqrt{3}\right)\left(1+\sqrt{5}+\sqrt{3}\right)\)
