\(tínhhợplí:\left(1,2-\sqrt{\dfrac{1}{4}:1\dfrac{1}{20}+\left|-\dfrac{3}{4}\right|-\left(-\dfrac{3}{2}\right)^2}\right)\)
Những câu hỏi liên quan
\(\left(\sqrt{\dfrac{1}{4}-1,2}\right):1\dfrac{1}{20}-\left(-\dfrac{5}{2}\right)^2+\left|1,25-\dfrac{3}{4}\right|\)
\(=\left(\dfrac{1}{2}-\dfrac{6}{5}\right):\dfrac{21}{20}-\dfrac{25}{4}+\dfrac{1}{2}=\dfrac{-7}{10}\cdot\dfrac{20}{21}-\dfrac{23}{4}\)
\(=\dfrac{-2}{3}-\dfrac{23}{4}=\dfrac{-8-69}{12}=-\dfrac{77}{12}\)
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rút gọn
g, \(\left(\dfrac{5-2\sqrt{5}}{2-\sqrt{5}}-2\right).\left(\dfrac{5+3\sqrt{5}}{3+\sqrt{5}}-2\right)\) h,\(\left(\dfrac{4}{3}\sqrt{3}+\sqrt{2}+\sqrt{3\dfrac{1}{3}}\right).\left(\sqrt{1,2}+\sqrt{2}-4\sqrt{\dfrac{1}{5}}\right)\)
g: \(=\left(-\sqrt{5}-2\right)\left(\sqrt{5}-2\right)\)
=-(căn 5+2)(căn 5-2)
=-(5-4)=-1
h: \(=\left(\dfrac{4}{3}\sqrt{3}+\sqrt{2}+\dfrac{\sqrt{30}}{3}\right)\left(\dfrac{\sqrt{30}}{5}+\sqrt{2}-\dfrac{4}{5}\sqrt{5}\right)\)
=4/5*căn 10+4/3*căn 6-16/15*căn 15+2/5*căn 15+2-4/5*căn 10+30/15+2/3*căn 15-4/3*căn 6
=4
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1 nhân chia căn bậc haia/left(dfrac{4}{3}sqrt{3}+sqrt{2}+sqrt{3dfrac{1}{3}}right)left(sqrt{1,2}+sqrt{2}-4sqrt{0,2}right)b/ left(dfrac{3x}{2}sqrt{dfrac{x}{2y}}-0,4sqrt{dfrac{2}{xy}}+dfrac{1}{3}sqrt{dfrac{xy}{2}}right):dfrac{4}{15}sqrt{dfrac{2x}{3y}}2 Cộng trừ căn bậc haia/ 0,1sqrt{200}-2sqrt{0,08}+4sqrt{0,5}+0,4sqrt{50}b/ dfrac{2}{3}xsqrt{9x}+6xsqrt{dfrac{x}{4}-x^2}sqrt{dfrac{1}{x}}
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1 nhân chia căn bậc hai
a/\(\left(\dfrac{4}{3}\sqrt{3}+\sqrt{2}+\sqrt{3\dfrac{1}{3}}\right)\left(\sqrt{1,2}+\sqrt{2}-4\sqrt{0,2}\right)\)
b/ \(\left(\dfrac{3x}{2}\sqrt{\dfrac{x}{2y}}-0,4\sqrt{\dfrac{2}{xy}}+\dfrac{1}{3}\sqrt{\dfrac{xy}{2}}\right):\dfrac{4}{15}\sqrt{\dfrac{2x}{3y}}\)
2 Cộng trừ căn bậc hai
a/ \(0,1\sqrt{200}-2\sqrt{0,08}+4\sqrt{0,5}+0,4\sqrt{50}\)
b/ \(\dfrac{2}{3}x\sqrt{9x}+6x\sqrt{\dfrac{x}{4}-x^2}\sqrt{\dfrac{1}{x}}\)
Bài 2:
a: \(=\sqrt{2}-\dfrac{2}{5}\sqrt{2}+2\sqrt{2}+2\sqrt{2}=\dfrac{23}{5}\sqrt{2}\)
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(\(\sqrt{\dfrac{1}{4}}\) - 1,2) : 1\(\dfrac{1}{20}\) - (- \(\dfrac{5}{2}\))2 + \(\left|1,25-\dfrac{3}{4}\right|\)
\(=\left(\dfrac{1}{2}-\dfrac{6}{5}\right):\dfrac{21}{20}-\dfrac{25}{4}+\dfrac{1}{2}\)
\(=\dfrac{-7}{10}\cdot\dfrac{20}{21}-\dfrac{25}{4}+\dfrac{2}{4}\)
\(=\dfrac{-2}{3}-\dfrac{23}{4}=\dfrac{-8-69}{12}=\dfrac{-77}{12}\)
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\(\left(\sqrt{\dfrac{1}{4}}-1,2\right):1\dfrac{1}{20}-\left(-\dfrac{5}{2}\right)^2+\left|1,25-\dfrac{3}{4}\right|\)
\(=-\dfrac{7}{10}:\dfrac{21}{20}-\dfrac{25}{4}+\left|\dfrac{1}{2}\right|\)
\(=-\dfrac{7}{10}.\dfrac{20}{21}-\dfrac{25}{4}+\dfrac{1}{2}\)
\(=-\dfrac{2}{3}-\dfrac{25}{4}+\dfrac{1}{2}\)
\(=-\dfrac{77}{12}\)
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Tính: a, \(\left(4\sqrt{2}-\dfrac{11}{2}\sqrt{8}-\dfrac{1}{3}\sqrt{288}+\sqrt{50}\right)\left(\dfrac{1}{2}\sqrt{2}\right)\)
b, \(\left(\dfrac{4}{5}\sqrt{5}-\dfrac{1}{3}\sqrt{\dfrac{1}{5}}+3\sqrt{20}+\dfrac{1}{2}\sqrt{245}\right)\div\sqrt{5}\)
a: Ta có: \(\left(4\sqrt{2}-\dfrac{11}{2}\sqrt{8}-\dfrac{1}{3}\sqrt{288}+\sqrt{50}\right)\cdot\left(\dfrac{1}{2}\sqrt{2}\right)\)
\(=\dfrac{1}{2}\sqrt{2}\cdot\left(4\sqrt{2}-11\sqrt{2}-4\sqrt{2}+5\sqrt{2}\right)\)
\(=\dfrac{1}{2}\sqrt{2}\cdot6\sqrt{2}=3\)
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15 tháng 12 2021 lúc 21:58
Thực hiện phép tính (tính nhanh nếu có thể):
4) \(4\cdot\left(\dfrac{-1}{2}\right)^3+\left|-1\dfrac{1}{2}+\sqrt{\dfrac{9}{4}}\right|:\sqrt{25}\)
5) \(\left[6-3\cdot\left(\dfrac{-1}{3}\right)^2+\sqrt{\dfrac{1}{4}}\right]:\sqrt{0,\left(9\right)}\)
a,dfrac{8^{20}+4^{20}}{4^{25}+64^5}b,left(1+dfrac{2}{3}-dfrac{1}{4}right).left(dfrac{4}{5}-dfrac{3}{4}right)^2c,23dfrac{1}{3}:left(dfrac{-5}{7}right)-13dfrac{1}{3}:left(dfrac{-5}{7}right)d,1:left(dfrac{2}{3}-dfrac{3}{4}right)^2e,dfrac{45^{10}.5^{20}}{75^{15}}
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a,\(\dfrac{8^{20}+4^{20}}{4^{25}+64^5}\)
b,\(\left(1+\dfrac{2}{3}-\dfrac{1}{4}\right).\left(\dfrac{4}{5}-\dfrac{3}{4}\right)^2\)
c,\(23\dfrac{1}{3}:\left(\dfrac{-5}{7}\right)-13\dfrac{1}{3}:\left(\dfrac{-5}{7}\right)\)
d,1:\(\left(\dfrac{2}{3}-\dfrac{3}{4}\right)^2\)
e,\(\dfrac{45^{10}.5^{20}}{75^{15}}\)
e: \(=\dfrac{5^{30}\cdot3^{20}}{3^{15}\cdot5^{30}}=3^5=243\)
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Chứng minh rằng:
\(\dfrac{1}{3\left(\sqrt{2}+1\right)}+\dfrac{1}{5\left(\sqrt{3}+\sqrt{2}\right)}+\dfrac{1}{7\left(\sqrt{4}+\sqrt{3}\right)}+...+\dfrac{1}{4021\left(\sqrt{2011}+\sqrt{2010}\right)}< \dfrac{1}{2}\left(1-\dfrac{1}{\sqrt{2011}}\right)\)
\(\dfrac{1}{\sqrt{k}+\sqrt{k+1}}=\dfrac{\sqrt{k}-\sqrt{k+1}}{k-k-1}=\sqrt{k+1}-\sqrt{k}\\ \Leftrightarrow\text{Đặt}\text{ }A=\dfrac{1}{3\left(\sqrt{2}+\sqrt{1}\right)}+\dfrac{1}{5\left(\sqrt{3}+\sqrt{2}\right)}+...+\dfrac{1}{4021\left(\sqrt{2011}+\sqrt{2010}\right)}< \dfrac{1}{2\left(\sqrt{2}+\sqrt{1}\right)}+\dfrac{1}{2\left(\sqrt{3}+\sqrt{2}\right)}+...+\dfrac{1}{2\left(\sqrt{2011}+\sqrt{2010}\right)}\\ \Leftrightarrow A< \dfrac{1}{2}\left(\dfrac{1}{\sqrt{2}+\sqrt{1}}+\dfrac{1}{\sqrt{3}+\sqrt{2}}+...+\dfrac{1}{\sqrt{2011}+\sqrt{2010}}\right)\)
\(\Leftrightarrow A< \dfrac{1}{2}\left(\sqrt{2}-\sqrt{1}+\sqrt{3}-\sqrt{2}+...+\sqrt{2011}-\sqrt{2010}\right)\\ \Leftrightarrow A< \dfrac{1}{2}\left(\sqrt{2011}-1\right)< \dfrac{1}{2}\cdot\dfrac{\sqrt{2011}-1}{\sqrt{2011}}=\dfrac{1}{2}\left(1-\dfrac{1}{\sqrt{2011}}\right)\)
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4.
\(A=\left(\dfrac{\sqrt{x}}{\sqrt{x}-1}\right)-\left(\dfrac{1}{x+\sqrt{x}}\right).\left(\dfrac{1}{\sqrt{x}-1}-\dfrac{2}{x-1}\right)\)
a. Rút gọn A.
b. Tính x khi \(A=\dfrac{1}{2}\)
5. CMR
\(\left(\dfrac{\sqrt{30}}{\sqrt{3}}-\dfrac{\sqrt{20}}{\sqrt{2}}-\dfrac{6}{\sqrt{6}}\right).\sqrt{4+\sqrt{15}}=2\)
nhanh lên nha
