Các câu hỏi tương tự
\(\dfrac{1}{2\sqrt{1}+1\sqrt{2}}+\dfrac{1}{3\sqrt{2}+2\sqrt{3}}+...+\dfrac{1}{2025\sqrt{2024}+2024\sqrt{2025}}\)
So sánh:
1) \(\dfrac{1}{4}\) và \(\dfrac{1}{1+2\sqrt{2}}\)
2)\(\sqrt{2018}+\sqrt{2025}\) và \(\sqrt{2026}+\sqrt{2024}\)
BT1: TínhA (frac{3}{2} .sqrt{6}+ 2sqrt{frac{2}{3}}- 4sqrt{frac{3}{2}}) . (3sqrt{frac{2}{3}}- sqrt{12}- sqrt{6}BT2: Rút gonA frac{1}{sqrt{1}+sqrt{2}}+ frac{1}{sqrt{2}+sqrt{3}}+ frac{1}{sqrt{3}+sqrt{4}}+ ....... + frac{1}{sqrt{2024}+sqrt{2025}}CM: B frac{1}{sqrt{1}}+ frac{1}{sqrt{2}}+ ...... + frac{1}{sqrt{2024}} 88BT3: Rút gọnC sqrt{2a+sqrt{4x-1}}+ sqrt{2a-sqrt{4a-1}}với frac{1}{4} a frac{1}{2}BT4:Hỏi M frac{sqrt{3-2sqrt{2}}}{sqrt{17-12sqrt{2}}}- frac{sqrt{3+2sqrt{2}}}{sqrt{17+12sqrt{2}}}có...
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BT1: Tính
A = (\(\frac{3}{2}\) .\(\sqrt{6}\)+ \(2\sqrt{\frac{2}{3}}\)- \(4\sqrt{\frac{3}{2}}\)) . (\(3\sqrt{\frac{2}{3}}\)- \(\sqrt{12}\)- \(\sqrt{6}\)
BT2: Rút gon
A = \(\frac{1}{\sqrt{1}+\sqrt{2}}\)+ \(\frac{1}{\sqrt{2}+\sqrt{3}}\)+ \(\frac{1}{\sqrt{3}+\sqrt{4}}\)+ ....... + \(\frac{1}{\sqrt{2024}+\sqrt{2025}}\)
CM: B = \(\frac{1}{\sqrt{1}}\)+ \(\frac{1}{\sqrt{2}}\)+ ...... + \(\frac{1}{\sqrt{2024}}\)> 88
BT3: Rút gọn
C = \(\sqrt{2a+\sqrt{4x-1}}\)+ \(\sqrt{2a-\sqrt{4a-1}}\)với \(\frac{1}{4}\)< a < \(\frac{1}{2}\)
BT4:
Hỏi M = \(\frac{\sqrt{3-2\sqrt{2}}}{\sqrt{17-12\sqrt{2}}}\)- \(\frac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)có phải là số tự nhiên không?
BT5:
Phân tích thành nhân tử: M = \(7\sqrt{x-1}\)- \(\sqrt{x^3-x^2}\)+ x - 1 (với x >=1)
GIÚP MÌNH VỚI Ạ MÌNH CẦN GẤP LẮM. CẨM ƠN NHIỀU ẠAAAAAAAA
So sánh 88 với biểu thức E với
\(E=\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{2023}}+\frac{1}{\sqrt{2024}}\)
SO SÁNH
a.\(\sqrt{n+2}-\sqrt{n+1}và\sqrt{n+1}-\sqrt{n}\left(n\right)làsốnguyêndương\)
\(b.\sqrt{17}+\sqrt{26}+1và\sqrt{99}\)
Chứng minh
\(c.\frac{1}{\sqrt{1}}+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+...+\frac{1}{\sqrt{2025}}>45\)
Rút gọn biểu thức:
\(y=\frac{1}{1+\sqrt{5}}+\frac{1}{\sqrt{5}+\sqrt{9}}+\frac{1}{\sqrt{9}+\sqrt{13}}+...\frac{1}{\sqrt{2021}+\sqrt{2025}}\)
So sánh: \(\frac{2012}{\sqrt{1}}+\frac{2012}{\sqrt{2}}+....+\frac{2012}{\sqrt{2025}}\) với \(30180\)
Tính giá trị biểu thức:text{a) }frac{1}{sqrt{1}+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+frac{1}{sqrt{3}+sqrt{4}}+frac{1}{sqrt{4}+sqrt{5}}+...+frac{1}{sqrt{2010}+sqrt{2011}}text{b) }frac{1}{2sqrt{1}+1sqrt{2}}+frac{1}{3sqrt{2}+2sqrt{3}}+frac{1}{4sqrt{3}+3sqrt{4}}+...+frac{1}{121sqrt{120}+120sqrt{121}}text{c) }sqrt{1+frac{1}{1^2}+frac{1}{2^2}}+sqrt{1+frac{1}{2^2}+frac{1}{3^2}}+sqrt{1+frac{1}{3^2}+frac{1}{4^2}}+...sqrt{+1+frac{1}{2010^2}+frac{1}{2011^2}}
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Tính giá trị biểu thức:
\(\text{a) }\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt{4}+\sqrt{5}}+...+\frac{1}{\sqrt{2010}+\sqrt{2011}}\)
\(\text{b) }\frac{1}{2\sqrt{1}+1\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{121\sqrt{120}+120\sqrt{121}}\)
\(\text{c) }\sqrt{1+\frac{1}{1^2}+\frac{1}{2^2}}+\sqrt{1+\frac{1}{2^2}+\frac{1}{3^2}}+\sqrt{1+\frac{1}{3^2}+\frac{1}{4^2}}+...\sqrt{+1+\frac{1}{2010^2}+\frac{1}{2011^2}}\)
Rút gọn biểu thức 1) frac{sqrt{5+2sqrt{6}}+sqrt{8+2sqrt{15}}}{sqrt{7+2sqrt{10}}}2) left(2+frac{3+sqrt{3}}{sqrt{3}+1}right)left(2+frac{3-sqrt{3}}{sqrt{3}-1}right):left(sqrt{5}-2right)3) left(frac{15}{sqrt{6}+1}+frac{4}{sqrt{6}-2}-frac{12}{3-sqrt{6}}right).left(sqrt{6}+11right)4) frac{1}{1+sqrt{2}}+frac{1}{sqrt{2}+sqrt{3}}+frac{1}{sqrt{3}+sqrt{4}}+...+frac{1}{sqrt{99}+sqrt{100}}5) frac{1}{1-sqrt{2}}-frac{1}{sqrt{2}-sqrt{3}}+frac{1}{sqrt{3}-sqrt{4}}-...-frac{1}{sqrt{98}-sqrt{99}}+frac{1}{sqrt{99}-s...
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Rút gọn biểu thức
1) \(\frac{\sqrt{5+2\sqrt{6}}+\sqrt{8+2\sqrt{15}}}{\sqrt{7+2\sqrt{10}}}\)
2) \(\left(2+\frac{3+\sqrt{3}}{\sqrt{3}+1}\right)\left(2+\frac{3-\sqrt{3}}{\sqrt{3}-1}\right):\left(\sqrt{5}-2\right)\)
3) \(\left(\frac{15}{\sqrt{6}+1}+\frac{4}{\sqrt{6}-2}-\frac{12}{3-\sqrt{6}}\right).\left(\sqrt{6}+11\right)\)
4) \(\frac{1}{1+\sqrt{2}}+\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+...+\frac{1}{\sqrt{99}+\sqrt{100}}\)
5) \(\frac{1}{1-\sqrt{2}}-\frac{1}{\sqrt{2}-\sqrt{3}}+\frac{1}{\sqrt{3}-\sqrt{4}}-...-\frac{1}{\sqrt{98}-\sqrt{99}}+\frac{1}{\sqrt{99}-\sqrt{100}}\)
6) \(\frac{1}{2+\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+...+\frac{1}{100\sqrt{99}+99\sqrt{100}}\)
7)\(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}+2\right)\left(\frac{\sqrt{2}+\sqrt{3}}{4\sqrt{2}}-\frac{\sqrt{3}}{\sqrt{2}+\sqrt{3}}\right)\left(24+8\sqrt{6}\right)\left(\frac{\sqrt{2}}{\sqrt{2}+\sqrt{3}}+\frac{\sqrt{3}}{\sqrt{2}-\sqrt{3}}\right)\)