Bài 8: Rút gọn biểu thức chứa căn bậc hai
Các câu hỏi tương tự
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}
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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) \(\dfrac{\sqrt{12}-6}{\sqrt{8}-\sqrt{24}}-\dfrac{3+\sqrt{3}}{\sqrt{3}}-\dfrac{4}{\sqrt{7}-1}\)
Làm mất căn mẫu và thu gọn
1) dfrac{sqrt{15}-sqrt{5}}{sqrt{3}-1}+dfrac{5-2sqrt{5}}{2sqrt{5}-4}
2) left(1-dfrac{5+sqrt{5}}{1+sqrt{5}}right)left(dfrac{5-sqrt{5}}{1-sqrt{5}}-1right)
3) left(dfrac{3sqrt{125}}{15}-dfrac{10-4sqrt{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{s...
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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~!
Bài : Thu gọn1) dfrac{3sqrt{5}-5sqrt{3}}{sqrt{15}-3}2) dfrac{sqrt{5+2sqrt{6}}}{sqrt{2}+sqrt{3}}3) dfrac{7+4sqrt{3}}{2+sqrt{3}}4) dfrac{16-6sqrt{7}}{sqrt{7}-3}5) dfrac{left(sqrt{3}-sqrt{2}right)^2+4sqrt{6}}{sqrt{3}+sqrt{2}}6) dfrac{left(sqrt{3}+2sqrt{5}right)^2-8sqrt{15}}{sqrt{6-2sqrt{10}}}
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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 các biểu thức:
1. sqrt{28}-2sqrt{252}+3sqrt{175}+3sqrt{567}
2. sqrt{left(sqrt{3}+1right)^2}+sqrt{7-4sqrt{3}}
3. sqrt{9-4sqrt{5}}-sqrt{dfrac{8}{7-3sqrt{5}}}
4. dfrac{sqrt{3}}{2-sqrt{3}}+dfrac{2}{2+sqrt{3}}
5. dfrac{2sqrt{2}+1}{1+sqrt{2}}+dfrac{1-2sqrt{2}}{1-sqrt{2}}+left(2-sqrt{3}right).left(2+sqrt{3}right)
6. sqrt{dfrac{2}{3-sqrt{5}}}+sqrt{dfrac{2}{7+sqrt{45}}}
7. dfrac{sqrt{2}}{sqrt{1+sqrt{2}}-1}-dfrac{sqrt{2}}{sqrt{1+sqrt{2}}+1}
8. sqrt{6-2sqrt{5}}+sqrt{dfrac{3-sqrt{5}}{3+sqrt{...
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Rút gọn các biểu thức:
1. \(\sqrt{28}-2\sqrt{252}+3\sqrt{175}+3\sqrt{567}\)
2. \(\sqrt{\left(\sqrt{3}+1\right)^2}+\sqrt{7-4\sqrt{3}}\)
3. \(\sqrt{9-4\sqrt{5}}-\sqrt{\dfrac{8}{7-3\sqrt{5}}}\)
4. \(\dfrac{\sqrt{3}}{2-\sqrt{3}}+\dfrac{2}{2+\sqrt{3}}\)
5. \(\dfrac{2\sqrt{2}+1}{1+\sqrt{2}}+\dfrac{1-2\sqrt{2}}{1-\sqrt{2}}+\left(2-\sqrt{3}\right).\left(2+\sqrt{3}\right)\)
6. \(\sqrt{\dfrac{2}{3-\sqrt{5}}}+\sqrt{\dfrac{2}{7+\sqrt{45}}}\)
7. \(\dfrac{\sqrt{2}}{\sqrt{1+\sqrt{2}}-1}-\dfrac{\sqrt{2}}{\sqrt{1+\sqrt{2}}+1}\)
8. \(\sqrt{6-2\sqrt{5}}+\sqrt{\dfrac{3-\sqrt{5}}{3+\sqrt{5}}}-\sqrt{\dfrac{3+\sqrt{5}}{3-\sqrt{5}}}\)
tính1.sqrt{147}+sqrt{54}-4sqrt{27}2.sqrt{28}-4sqrt{63}+7sqrt{112}3.sqrt{49}-5sqrt{28}+dfrac{1}{2}sqrt{63}4.left(2sqrt{6}-4sqrt{3}-dfrac{1}{4}sqrt{8}right).3sqrt{6}5.(2sqrt{1dfrac{9}{16}}-5sqrt{5dfrac{1}{16}}):sqrt{16}6.left(sqrt{48}-3sqrt{27}-sqrt{147}right):sqrt{3}7.left(sqrt{50}-3sqrt{49}right):sqrt{2}-sqrt{162}:sqrt{2}8.left(2sqrt{1dfrac{9}{10}}-sqrt{5dfrac{1}{10}}right):sqrt{10}9.2sqrt{dfrac{16}{3}}-3sqrt{dfrac{1}{27}}-6sqrt{dfrac{4}{75}}10.2sqrt{27}-6sqrt{dfrac{4}{3}}+dfrac{3}{5}sqrt{75}11....
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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.\(\left(1+\sqrt{5}-\sqrt{3}\right)\left(1+\sqrt{5}+\sqrt{3}\right)\)
Giải bài đầy đủ giùm mình, đừng viết tắt.1) dfrac{1}{3-2sqrt{2}}-dfrac{1}{3+2sqrt{2}}2)dfrac{1}{sqrt{2}-sqrt{3}}-dfrac{3}{sqrt{18}+2sqrt{3}}3)dfrac{2}{sqrt{5}-2}+dfrac{-2}{sqrt{5}+2}4)dfrac{3}{1-sqrt{2}}+dfrac{sqrt{2}-1}{sqrt{2}+1}5)dfrac{sqrt{7}+sqrt{5}}{sqrt{7}-sqrt{5}}-dfrac{sqrt{7}-sqrt{5}}{sqrt{7}+sqrt{5}}
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Giải bài đầy đủ giùm mình, đừng viết tắt.
1) \(\dfrac{1}{3-2\sqrt{2}}-\dfrac{1}{3+2\sqrt{2}}\)
2)\(\dfrac{1}{\sqrt{2}-\sqrt{3}}-\dfrac{3}{\sqrt{18}+2\sqrt{3}}\)
3)\(\dfrac{2}{\sqrt{5}-2}+\dfrac{-2}{\sqrt{5}+2}\)
4)\(\dfrac{3}{1-\sqrt{2}}+\dfrac{\sqrt{2}-1}{\sqrt{2}+1}\)
5)\(\dfrac{\sqrt{7}+\sqrt{5}}{\sqrt{7}-\sqrt{5}}-\dfrac{\sqrt{7}-\sqrt{5}}{\sqrt{7}+\sqrt{5}}\)
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) \(\dfrac{7+4\sqrt{3}}{2+\sqrt{3}}\)
tính1.left(sqrt{15}-2sqrt{3}right)^2+12sqrt{5}2.3sqrt{2}left(4-sqrt{2}right)+3left(1-2sqrt{2}right)^23.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)^25.left(sqrt{sqrt{14}+sqrt{5}}+sqrt{sqrt{14}-sqrt{5}}right)^26.left(sqrt{3}+1right)^3-left(sqrt{3}-1right)^37.left(sqrt{2}+1right)^3-left(sqrt{2}-1right)^38.sqrt{13-sqrt{160}}-sqrt{53+4sqrt{90}}9.sqrt{3-sqrt{5}}+sqrt{3+sqrt{5}}
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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.\(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\)
bài 3 : rút gọn P = \(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-\dfrac{1}{\sqrt{4}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{9}}\)