\(\dfrac{\sqrt{6+2\sqrt{5}}}{\sqrt{5}+1}=\dfrac{\sqrt{5+2\sqrt{5}+1}}{\sqrt{5}+1}=\dfrac{\sqrt{5}+1}{\sqrt{5}+1}=1\)
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Bài 1: Căn bậc hai
Cách khác Các câu hỏi tương tự
Tính:
a) dfrac{sqrt{7}-5}{2}-dfrac{6-2sqrt{7}}{4}+dfrac{6}{sqrt{7}-2}-dfrac{5}{4+sqrt{7}}
b) dfrac{2}{sqrt{6}-2}+dfrac{2}{sqrt{6}+2}+dfrac{5}{sqrt{6}}
c) dfrac{1}{sqrt{3}}+dfrac{1}{3sqrt{2}}+dfrac{1}{sqrt{3}}sqrt{dfrac{5}{12}-dfrac{1}{sqrt{6}}}
d) dfrac{2sqrt{3-sqrt{3+sqrt{13+sqrt{48}}}}}{sqrt{6}-sqrt{2}}
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Tính:
a) \(\dfrac{\sqrt{7}-5}{2}-\dfrac{6-2\sqrt{7}}{4}+\dfrac{6}{\sqrt{7}-2}-\dfrac{5}{4+\sqrt{7}}\)
b) \(\dfrac{2}{\sqrt{6}-2}+\dfrac{2}{\sqrt{6}+2}+\dfrac{5}{\sqrt{6}}\)
c) \(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)
d) \(\dfrac{2\sqrt{3-\sqrt{3+\sqrt{13+\sqrt{48}}}}}{\sqrt{6}-\sqrt{2}}\)
Rút gọn:a) 2sqrt{98}-3sqrt{18}+dfrac{1}{2}sqrt{32}b)left(5sqrt{2}+2sqrt{5}right).sqrt{5}-sqrt{250}c)left(2sqrt{3}-5sqrt{2}right).sqrt{3}-sqrt{36}d)3sqrt{48}+2sqrt{27}-dfrac{1}{3}sqrt{243}e) 6sqrt{dfrac{1}{3}}+dfrac{9}{sqrt{3}}-dfrac{2}{sqrt{3}-1}f)4sqrt{dfrac{1}{2}}-dfrac{6}{sqrt{2}}dfrac{2}{sqrt{2}+1}
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Rút gọn:
a) \(2\sqrt{98}-3\sqrt{18}+\dfrac{1}{2}\sqrt{32}\)
b)\(\left(5\sqrt{2}+2\sqrt{5}\right).\sqrt{5}-\sqrt{250}\)
c)\(\left(2\sqrt{3}-5\sqrt{2}\right).\sqrt{3}-\sqrt{36}\)
d)\(3\sqrt{48}+2\sqrt{27}-\dfrac{1}{3}\sqrt{243}\)
e) \(6\sqrt{\dfrac{1}{3}}+\dfrac{9}{\sqrt{3}}-\dfrac{2}{\sqrt{3}-1}\)
f)\(4\sqrt{\dfrac{1}{2}}-\dfrac{6}{\sqrt{2}}\dfrac{2}{\sqrt{2}+1}\)
Rút gọn biểu thức
\(\dfrac{1}{3-\sqrt{8}}-\dfrac{1}{\sqrt{8}-\sqrt{7}}+\dfrac{1}{\sqrt{7}-\sqrt{6}}-\dfrac{1}{\sqrt{6}-\sqrt{5}}+\dfrac{1}{\sqrt{5}-2}\)
Tính:
E=(\(\sqrt{18}-3\sqrt{6}+\sqrt{2}\)) \(\sqrt{2}+6\sqrt{3}\)
G=\(\left(2\sqrt{2}-\sqrt{5}+\sqrt{18}\right)\).\(\left(\sqrt{50}+\sqrt{5}\right)\)
H=\(\dfrac{2+\sqrt{2}}{\sqrt{2}+1}\).\(\dfrac{2-\sqrt{2}}{\sqrt{2}-1}\)
Thực hiện phép tính:
a. \(2\sqrt{16}+\sqrt{2}.\sqrt{0,02}-\dfrac{\sqrt{12,1}}{\sqrt{0,1}}\)
b. \(5\sqrt{20}-4\sqrt{45}+\dfrac{15}{\sqrt{5}}\)
c. \(\left(\dfrac{\sqrt{6}-\sqrt{3}}{5\sqrt{2}-5}+\dfrac{\sqrt{5}}{5}\right):\dfrac{2}{\sqrt{5}-\sqrt{3}}\)
d. \(\dfrac{\sqrt{6}-3}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}\)
thực hiện phép tính:
1, dfrac{sqrt{15}-sqrt{5}}{sqrt{3}-1}-dfrac{5-2sqrt{5}}{2sqrt{5}-4}
2,dfrac{sqrt{3}+1}{sqrt{3}-1}+dfrac{sqrt{3}-1}{sqrt{3}+1}
3,dfrac{2sqrt{8}-sqrt{12}}{sqrt{18}-sqrt{48}}+dfrac{sqrt{5}+sqrt{27}}{sqrt{30}-sqrt{2}}
4,dfrac{3-sqrt{3}}{2sqrt{3}-1}+dfrac{3+sqrt{3}}{2sqrt{3}-1}
5,dfrac{2sqrt{3}-4}{sqrt{3}-1}+dfrac{2sqrt{2}-1}{sqrt{2}-1}-dfrac{1+sqrt{6}}{sqrt{2}+sqrt{3}}
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thực hiện phép tính:
1, \(\dfrac{\sqrt{15}-\sqrt{5}}{\sqrt{3}-1}-\dfrac{5-2\sqrt{5}}{2\sqrt{5}-4}\)
2,\(\dfrac{\sqrt{3}+1}{\sqrt{3}-1}+\dfrac{\sqrt{3}-1}{\sqrt{3}+1}\)
3,\(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}+\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}-\sqrt{2}}\)
4,\(\dfrac{3-\sqrt{3}}{2\sqrt{3}-1}+\dfrac{3+\sqrt{3}}{2\sqrt{3}-1}\)
5,\(\dfrac{2\sqrt{3}-4}{\sqrt{3}-1}+\dfrac{2\sqrt{2}-1}{\sqrt{2}-1}-\dfrac{1+\sqrt{6}}{\sqrt{2}+\sqrt{3}}\)
Thực hiện các phép tính:
a. \(2\sqrt{16}+\sqrt{2}.\sqrt{0.02}-\dfrac{\sqrt{12,1}}{\sqrt{0,1}}\)
b. \(5\sqrt{20}-4\sqrt{45}+\dfrac{15}{\sqrt{5}}\)
c. \(\left(\dfrac{\sqrt{6}-\sqrt{3}}{5\sqrt{2}-5}+\dfrac{\sqrt{5}}{5}\right):\dfrac{2}{\sqrt{5}-\sqrt{3}}\)
d. \(\dfrac{\sqrt{6}-3}{\sqrt{3}-\sqrt{2}}-\dfrac{4}{\sqrt{3}+1}+3\sqrt{3}\)
Bài 1. Tính
a) A left[dfrac{6+sqrt{20}}{3+sqrt{5}}+dfrac{sqrt{14}-sqrt{2}}{sqrt{7}-1}right] : (2+ sqrt{2})
b) B sqrt{5-2sqrt{6}}+sqrt{5+2sqrt{6}}-dfrac{11}{2sqrt{3}+1}
Bài 2.
Cho A left(dfrac{sqrt{2}+sqrt{3}}{sqrt{2}-sqrt{3}}-dfrac{sqrt{2}-sqrt{3}}{sqrt{2}+sqrt{3}}right).dfrac{sqrt{3}-1}{3sqrt{2}-sqrt{6}}
Chứng minh A là số nguyên.
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Bài 1. Tính
a) A= \(\left[\dfrac{6+\sqrt{20}}{3+\sqrt{5}}+\dfrac{\sqrt{14}-\sqrt{2}}{\sqrt{7}-1}\right]\) : (2+ \(\sqrt{2}\))
b) B= \(\sqrt{5-2\sqrt{6}}+\sqrt{5+2\sqrt{6}}-\dfrac{11}{2\sqrt{3}+1}\)
Bài 2.
Cho A= \(\left(\dfrac{\sqrt{2}+\sqrt{3}}{\sqrt{2}-\sqrt{3}}-\dfrac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right).\dfrac{\sqrt{3}-1}{3\sqrt{2}-\sqrt{6}}\)
Chứng minh A là số nguyên.
Thực hiện phép tính :\(\sqrt{\dfrac{5+2\sqrt{6}}{5-\sqrt{6}}}+\sqrt{\dfrac{5-2\sqrt{6}}{5+\sqrt{6}}}\)
a.(\(\sqrt{6}+\sqrt{2}\) ).(\(\sqrt{3}-\sqrt{2}\) ).\(\sqrt{\sqrt{3}+2}\)
b.\(\dfrac{1}{\sqrt{3}}+\dfrac{1}{3\sqrt{2}}+\dfrac{1}{\sqrt{3}}\sqrt{\dfrac{5}{12}-\dfrac{1}{\sqrt{6}}}\)