`((sqrt 7(sqrt 2 - 1))/(sqrt 2 - 1) + (sqrt5(sqrt3-1))/(sqrt 3 - 1)) . (sqrt 7 - sqrt 5)`
`= (sqrt 7 + sqrt 5)(sqrt 7 - sqrt 5)`
`= 7 - 5 = 2`.
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Các câu hỏi tương tự
B1:Tínha,sqrt{left(4-sqrt{17}right)^2}-left(sqrt{17}+2right) b,dfrac{7}{sqrt{3}-sqrt{2}}-sqrt{147}-2sqrt{18}c,dfrac{6}{sqrt{5}-2}-dfrac{6}{sqrt{5}+2}+sqrt{8}-4sqrt{dfrac{1}{7}} ; left(dfrac{1}{2}sqrt{dfrac{1}{2}}-dfrac{3}{2}sqrt{2}+dfrac{4}{5}sqrt{200}right):dfrac{1}{8}
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B1:Tính
a,\(\sqrt{\left(4-\sqrt{17}\right)^2}-\left(\sqrt{17}+2\right)\) b,\(\dfrac{7}{\sqrt{3}-\sqrt{2}}-\sqrt{147}-2\sqrt{18}\)
c,\(\dfrac{6}{\sqrt{5}-2}-\dfrac{6}{\sqrt{5}+2}+\sqrt{8}-4\sqrt{\dfrac{1}{7}}\) ; \(\left(\dfrac{1}{2}\sqrt{\dfrac{1}{2}}-\dfrac{3}{2}\sqrt{2}+\dfrac{4}{5}\sqrt{200}\right):\dfrac{1}{8}\)
chứng minh đẳng thức: \(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)= -2
7 tháng 9 2023 lúc 22:51
Thực hiện phép tính và thu gọn biểu thức:
B= \(\left(\dfrac{4}{1-\sqrt{5}}+\dfrac{1}{2+\sqrt{5}}-\dfrac{4}{3-\sqrt{5}}\right)\left(\sqrt{5}-6\right)\)
Thực hiện phép tính:
\(\sqrt{48}-\dfrac{\sqrt{21}-\sqrt{15}}{\sqrt{7}-\sqrt{5}}+\dfrac{2}{\sqrt{3}+1}\)
a) A=\(\left(\dfrac{2+\sqrt{2}}{\sqrt{2}+1}-\dfrac{\sqrt{15}-\sqrt{35}}{\sqrt{3}-\sqrt{7}}\right).\left(\sqrt{2}+\sqrt{5}\right)\)
b) B=\(\dfrac{12}{3+\sqrt{3}}-\dfrac{6}{\sqrt{3}}+\dfrac{\sqrt{27}-3\sqrt{2}}{\sqrt{3}.\sqrt{2}}\)
c)C=\(\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}}\right).\left(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-\dfrac{\sqrt{x}+2}{\sqrt{x}-1}\right)\)(x>0,x≠1,x≠4)
dfrac{sqrt{3-sqrt{5}}left(3+sqrt{5}right)}{sqrt{10}+sqrt{2}}dfrac{10+2sqrt{10}}{sqrt{5}+sqrt{2}}+dfrac{8}{1-sqrt{5}}dfrac{5+sqrt{7}}{9-sqrt{23+8sqrt{7}}}+dfrac{5-sqrt{7}}{2+sqrt{16+6sqrt{7}}}dfrac{1}{sqrt{2}+sqrt{2+sqrt{3}}}+dfrac{1}{sqrt{2}-sqrt{2+sqrt{3}}}
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\(\dfrac{\sqrt{3-\sqrt{5}}\left(3+\sqrt{5}\right)}{\sqrt{10}+\sqrt{2}}\)
\(\dfrac{10+2\sqrt{10}}{\sqrt{5}+\sqrt{2}}\)+\(\dfrac{8}{1-\sqrt{5}}\)
\(\dfrac{5+\sqrt{7}}{9-\sqrt{23+8\sqrt{7}}}\)+\(\dfrac{5-\sqrt{7}}{2+\sqrt{16+6\sqrt{7}}}\)
\(\dfrac{1}{\sqrt{2}+\sqrt{2+\sqrt{3}}}\)+\(\dfrac{1}{\sqrt{2}-\sqrt{2+\sqrt{3}}}\)
Rút gọn các biểu thức sau:a. dfrac{8}{left(sqrt{5}+sqrt{3}right)^2} - dfrac{8}{left(sqrt{5}-sqrt{3}right)^2}b.dfrac{1}{4-3sqrt{2}} - dfrac{1}{4+3sqrt{2}}c.left(dfrac{sqrt{7}+3}{sqrt{7}-3}-dfrac{sqrt{7}-3}{sqrt{7}+3}right): sqrt{28}d.dfrac{3}{sqrt{6}-sqrt{3}}+dfrac{4}{sqrt{7}+sqrt{3}}
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Rút gọn các biểu thức sau:
a. \(\dfrac{8}{\left(\sqrt{5}+\sqrt{3}\right)^2}\) - \(\dfrac{8}{\left(\sqrt{5}-\sqrt{3}\right)^2}\)
b.\(\dfrac{1}{4-3\sqrt{2}}\) - \(\dfrac{1}{4+3\sqrt{2}}\)
c.\(\left(\dfrac{\sqrt{7}+3}{\sqrt{7}-3}-\dfrac{\sqrt{7}-3}{\sqrt{7}+3}\right)\): \(\sqrt{28}\)
d.\(\dfrac{3}{\sqrt{6}-\sqrt{3}}\)+\(\dfrac{4}{\sqrt{7}+\sqrt{3}}\)
\(\dfrac{1}{3\left(1+\sqrt{2}\right)}+\dfrac{1}{5\left(\sqrt{2}+\sqrt{3}\right)}+\dfrac{1}{7\left(\sqrt{3}+\sqrt{4}\right)}+...+\dfrac{1}{97\left(\sqrt{48}+\sqrt{49}\right)}< \dfrac{7}{3}\)
chứng minh rằng:\(\dfrac{1}{3\left(\sqrt{1}+\sqrt{2}\right)}+\dfrac{1}{5\left(\sqrt{2}+\sqrt{3}\right)}+\dfrac{1}{7\left(\sqrt{3}+\sqrt{4}\right)}+...+\dfrac{1}{97\left(\sqrt{48}+\sqrt{49}\right)}< \dfrac{3}{7}\)
1)Tìm x để căn thức sau có nghĩa
a)\(\sqrt{2x-4}\) b)\(\sqrt{\dfrac{-7}{4-x}}\)
2) Tính
A=\(\sqrt{9+4\sqrt{5}}-\sqrt{9-4\sqrt{5}}
\)
B=\(\left(\dfrac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\dfrac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\dfrac{1}{\sqrt{7}-\sqrt{5}}\)
Helpppp
Chứng minh đẳng thức
\(\left(4-\sqrt{7}\right)^2=23-8\sqrt{7}\)
\(\sqrt{9-4\sqrt{5}}-\sqrt{5}=-2\)
\(\dfrac{\sqrt{4-2\sqrt{3}}}{1+\sqrt{2}}:\dfrac{\sqrt{2}-1}{\sqrt{3}+1}=2\)
\(\left(\dfrac{2\sqrt{3}-\sqrt{6}}{\sqrt{8}-2}-\dfrac{\sqrt{216}}{3}\right).\dfrac{1}{\sqrt{6}}=-1,5\)