\(\sqrt{206}^{3 }\cdot132+3^{^{ }4}\)\(\cdot\dfrac{4392}{7362}\)
Những câu hỏi liên quan
\(\dfrac{\sqrt{8-4\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{4\cdot2-4\sqrt{3}}}{\sqrt{2}}=\dfrac{\sqrt{4}\cdot\sqrt{2-\sqrt{3}}}{\sqrt{2}}=\sqrt{2}\cdot\sqrt{2-\sqrt{3}}\)
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) \(\left[6-3\cdot\left(\dfrac{-1}{3}\right)^2+\sqrt{\dfrac{1}{4}}\right]:\sqrt{0,\left(9\right)}\)
2 tháng 12 2023 lúc 20:18
\(\sqrt{\dfrac{16}{49}}+\left(\dfrac{1}{2}\right)^3-\left|-\dfrac{4}{7}\right|-\dfrac{7}{8}\)
\(\left|\dfrac{1}{2}-\dfrac{3}{5}\right|\cdot\sqrt{9}+0.5\cdot\left(-2\dfrac{3}{5}\right)\)
\(\sqrt{\dfrac{16}{49}}+\left(\dfrac{1}{2}\right)^3-\left|-\dfrac{4}{7}\right|-\dfrac{7}{8}\)
\(=\dfrac{4}{7}+\dfrac{1}{8}-\dfrac{4}{7}-\dfrac{7}{8}\)
\(=\dfrac{1}{8}-\dfrac{7}{8}=-\dfrac{6}{8}=-\dfrac{3}{4}\)
\(\left|\dfrac{1}{2}-\dfrac{3}{5}\right|\cdot\sqrt{9}+0,5\left(-2\dfrac{3}{5}\right)\)
\(=\left|\dfrac{5-6}{10}\right|\cdot3+\dfrac{1}{2}\cdot\dfrac{-13}{5}\)
\(=\dfrac{1}{10}\cdot3+\dfrac{1}{2}\cdot\dfrac{-13}{5}\)
\(=\dfrac{3}{10}-\dfrac{13}{10}=-\dfrac{10}{10}=-1\)
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CMR":
\(\dfrac{1}{3}\cdot\dfrac{4}{6}\cdot\dfrac{7}{9}\cdot.......\cdot\dfrac{\left(3n-2\right)}{3n}\cdot\dfrac{\left(3n+1\right)}{3n+3}< \dfrac{1}{3\sqrt{n+1}}\)
\(\dfrac{3}{5}+\dfrac{\left(-1\right)}{4},\dfrac{|-3|}{5}\cdot\dfrac{4}{9}+\dfrac{\left(-4\right)}{9},\sqrt{16}+\sqrt{25}\)
Tính:
\(\left(\dfrac{3\sqrt{3}-2\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\dfrac{3\sqrt{2}+2\sqrt{3}}{\sqrt{3}+\sqrt{2}}\right)\cdot\dfrac{5-2\sqrt{6}}{4}\)
Ta có: \(\left(\dfrac{3\sqrt{3}-2\sqrt{2}}{\sqrt{3}-\sqrt{2}}+\dfrac{3\sqrt{2}+2\sqrt{3}}{\sqrt{3}+\sqrt{2}}\right)\cdot\dfrac{5-2\sqrt{6}}{4}\)
\(=\left(\dfrac{\left(\sqrt{3}-\sqrt{2}\right)\left(3+\sqrt{6}+2\right)}{\sqrt{3}-\sqrt{2}}+\dfrac{\sqrt{6}\left(\sqrt{3}+\sqrt{2}\right)}{\sqrt{3}+\sqrt{2}}\right)\cdot\dfrac{5-2\sqrt{6}}{4}\)
\(=\left(5+\sqrt{6}+\sqrt{6}\right)\cdot\dfrac{5-2\sqrt{6}}{4}\)
\(=\dfrac{\left(5+2\sqrt{6}\right)\left(5-2\sqrt{6}\right)}{4}\)
\(=\dfrac{25-24}{4}=\dfrac{1}{4}\)
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Cho :
\(P=\dfrac{\sqrt{a}\cdot\left(16-\sqrt{a}\right)}{a-4}+\dfrac{3+2\cdot\sqrt{a}}{2-\sqrt{a}}-\dfrac{2-3\cdot\sqrt{a}}{\sqrt{a}+2}\)
a) Rút gọn P
b) Tính giá trị của P tại \(a=4+2\cdot\sqrt{3}\)
c) Tìm min \(Q=P+\sqrt{a}\)
a: \(P=\dfrac{16\sqrt{a}-a-\left(2\sqrt{a}+3\right)\left(\sqrt{a}+2\right)+\left(3\sqrt{a}-2\right)\left(\sqrt{a}-2\right)}{a-4}\)
\(=\dfrac{16\sqrt{a}-a-2a-7\sqrt{a}-6+3a-8\sqrt{a}+4}{a-4}\)
\(=\dfrac{\sqrt{a}-2}{a-4}=\dfrac{1}{\sqrt{a}+2}\)
b: Thay \(a=4+2\sqrt{3}\) vào P, ta được:
\(P=\dfrac{1}{\sqrt{3}+1+2}=\dfrac{1}{3+\sqrt{3}}=\dfrac{3-\sqrt{3}}{6}\)
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D sqrt{94-42sqrt{5}}-sqrt{94+42sqrt{5}}
A sqrt{sqrt{5}-sqrt{3-sqrt{29-12sqrt{5}}}}
C dfrac{2sqrt{4-sqrt{5+sqrt{21+sqrt{80}}}}}{sqrt{10}-sqrt{2}}
F sqrt{2+sqrt{3}}cdotsqrt{2+sqrt{2+sqrt{3}}cdotsqrt{2+sqrt{2+sqrt{2+sqrt{3}}}}}cdotsqrt{2-sqrt{2+sqrt{2+sqrt{3}}}}
B dfrac{1}{sqrt{1}+sqrt{2}}+dfrac{1}{sqrt{2}+sqrt{3}}+dfrac{1}{sqrt{3}+sqrt{4}}+...+dfrac{1}{sqrt{n-1}+sqrt{n}}
E dfrac{1}{sqrt{1}-sqrt{2}}-dfrac{1}{sqrt{2}-sqrt{3}}+dfrac{1}{sqrt{3}-sqrt{4}}-...-dfrac{1}{sqrt{24}-sqrt{25}}
Đọc tiếp
D = \(\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)
A = \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
C = \(\dfrac{2\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}\)
F = \(\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{3}}\cdot\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{3}}}}}\cdot\sqrt{2-\sqrt{2+\sqrt{2+\sqrt{3}}}}\)
B = \(\dfrac{1}{\sqrt{1}+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+...+\dfrac{1}{\sqrt{n-1}+\sqrt{n}}\)
E = \(\dfrac{1}{\sqrt{1}-\sqrt{2}}-\dfrac{1}{\sqrt{2}-\sqrt{3}}+\dfrac{1}{\sqrt{3}-\sqrt{4}}-...-\dfrac{1}{\sqrt{24}-\sqrt{25}}\)
C = \(\dfrac{2\sqrt{4-\sqrt{5+\sqrt{21+\sqrt{80}}}}}{\sqrt{10}-\sqrt{2}}\)
C = \(\dfrac{2\sqrt{4-\sqrt{5+\sqrt{\left(\sqrt{20}+1\right)^2}}}}{\sqrt{10}-\sqrt{2}}\)
C = \(\dfrac{2\sqrt{4-\sqrt{6+\sqrt{20}}}}{\sqrt{10}-\sqrt{2}}\) = \(\dfrac{2\sqrt{4-\sqrt{\left(\sqrt{5}+1\right)^2}}}{\sqrt{10}-\sqrt{2}}\)
C = \(\dfrac{2\sqrt{3-\sqrt{5}}}{\sqrt{10}-\sqrt{2}}\) = \(\dfrac{2\sqrt{3-\sqrt{5}}\left(\sqrt{10}+\sqrt{2}\right)}{10-2}\)
C = \(\dfrac{2\sqrt{30-10\sqrt{5}}+2\sqrt{6-2\sqrt{5}}}{8}\)
C = \(\dfrac{2\sqrt{\left(5-\sqrt{5}\right)^2}+2\sqrt{\left(\sqrt{5}-1\right)^2}}{8}\)
C = \(\dfrac{2\left(5-\sqrt{5}\right)+2\left(\sqrt{5}-1\right)}{8}\)
C = \(\dfrac{10-2\sqrt{5}+2\sqrt{5}-2}{8}\) = \(\dfrac{8}{8}\) = \(1\)
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D = \(\sqrt{94-42\sqrt{5}}-\sqrt{94+42\sqrt{5}}\)
D = \(\sqrt{\left(7-3\sqrt{5}\right)^2}-\sqrt{\left(7+3\sqrt{5}\right)^2}\)
D = \(7-3\sqrt{5}-\left(7+3\sqrt{5}\right)\) = \(7-3\sqrt{5}-7-3\sqrt{5}\)
D = \(-6\sqrt{5}\)
A = \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)
A = \(\sqrt{\sqrt{5}-\sqrt{3-\sqrt{\left(2\sqrt{5}-3\right)^2}}}\)
A = \(\sqrt{\sqrt{5}-\sqrt{6-2\sqrt{5}}}\) = \(\sqrt{\sqrt{5}-\sqrt{\left(\sqrt{5}-1\right)^2}}\)
A = \(\sqrt{\sqrt{5}-\sqrt{5}+1}\) = \(\sqrt{1}=1\)
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tính: \((\dfrac{\sqrt{4}}{3}-\sqrt{3}+\dfrac{\sqrt{25}}{3})\cdot\sqrt{12}\)
\(=\left(\right)\dfrac{2+5}{3}-\sqrt{3}\) ).2\(\sqrt{3}\)
=\(\dfrac{14}{\sqrt{3}}-6\)
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