Thực hiện phép tính sau đây
\(\left(\sqrt{12}+2\sqrt{27}\right)\frac{\sqrt{3}}{2}-\sqrt{150}\)
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Thực hiện các phép tính sau đây
\(\frac{\sqrt{3}+\sqrt{2}-1}{2+\sqrt{6}}+\frac{\sqrt{2}-\sqrt{3}}{\sqrt{2}+1}\left(\frac{\sqrt{3}}{2-\sqrt{6}}+\frac{\sqrt{3}}{2+\sqrt{6}}-\frac{1}{\sqrt{2}}\right)\)
1. thực hiện phép tính
a, A=\(2\sqrt{3}-\sqrt{12}-\sqrt{9}\)
b,B=\(\sqrt{3}\left(\sqrt{12}+\sqrt{27}\right)\)
a, \(A=2\sqrt{3}-\sqrt{12}-\sqrt{9}\)
\(=2\sqrt{3}-2\sqrt{3}-3=-3\)
b, \(B=\sqrt{3}\left(\sqrt{12}+\sqrt{27}\right)\)
\(=\sqrt{3}\left(2\sqrt{3}+3\sqrt{3}\right)\)
\(=\sqrt{3}.5\sqrt{3}=5.3=15\)
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Thực hiện phép tính: \(\left(\sqrt{4,5}-\frac{1}{2}\sqrt{72}+5\sqrt{\frac{1}{2}}\right)\left(42\sqrt{\frac{25}{6}}-10\sqrt{\frac{3}{2}}-12\sqrt{\frac{98}{3}}\right)\)
\(\left(\sqrt{4,5}-\frac{1}{2}.\sqrt{72}+5\sqrt{\frac{1}{2}}\right).\left(42\sqrt{\frac{25}{6}}-10\sqrt{\frac{3}{2}}-12\sqrt{\frac{98}{3}}\right)\)
=\(\left(\frac{3\sqrt{2}}{2}-3\sqrt{2}+\frac{5\sqrt{2}}{2}\right).\left(35\sqrt{6}-5\sqrt{6}-28\sqrt{6}\right)\)
=\(\left(\frac{3\sqrt{2}-6\sqrt{2}+5\sqrt{2}}{2}\right).2\sqrt{6}\)
=\(2\sqrt{2}.\sqrt{6}=4\sqrt{3}\)
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Thực hiện phép tính: \(\left(\sqrt{4,5}-\frac{1}{2}\sqrt{72}+5\sqrt{\frac{1}{2}}\right)\left(42\sqrt{\frac{25}{6}}-10\sqrt{\frac{3}{2}}-12\sqrt{\frac{98}{3}}\right)\)
thực hiện phép tính:
\(\left(\sqrt{3}-2\right)\times\left(\sqrt{6}+\sqrt{2}\right)\sqrt{2+\sqrt{3}}\)
\(\sqrt{\frac{\sqrt{5}}{8\sqrt{5}+3\sqrt{35}}}\times\left(3\sqrt{2}+\sqrt{14}\right)\)
Thực hiện phép tính:
a) \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
b) \(\left(1+\sqrt{2}+\sqrt{3}\right)\left(1-\sqrt{2}-\sqrt{3}\right)\)
a) Ta có: \(\dfrac{2\sqrt{8}-\sqrt{12}}{\sqrt{18}-\sqrt{48}}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{30}+\sqrt{162}}\)
\(=\dfrac{-2\left(\sqrt{3}-\sqrt{8}\right)}{\sqrt{6}\left(\sqrt{3}-\sqrt{6}\right)}-\dfrac{\sqrt{5}+\sqrt{27}}{\sqrt{6}\left(\sqrt{5}+\sqrt{27}\right)}\)
\(=\dfrac{-3}{\sqrt{6}}=\dfrac{-3\sqrt{6}}{6}=\dfrac{-\sqrt{6}}{2}\)
b) Ta có: \(\left(1+\sqrt{2}+\sqrt{3}\right)\left(1-\sqrt{2}-\sqrt{3}\right)\)
\(=1-\left(\sqrt{2}+\sqrt{3}\right)^2\)
\(=1-5-2\sqrt{6}\)
\(=-4-2\sqrt{6}\)
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Thực hiện phép tính
A = \(\frac{1}{2}\sqrt{5\frac{1}{3}}-\sqrt{243}+\sqrt{147}+\frac{1}{2}\sqrt{27}\)
B = \(\sqrt{\left(\sqrt{5}-3\right)^2}+\sqrt{\left(1+\sqrt{5}\right)^2}\)
1. Rút gọn biểu thức:
\(D=\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)
2. Thực hiện phép tính rồi rút gọn:
\(A=\left(\sqrt{32}-\sqrt{50}+\sqrt{27}\right).\left(\sqrt{27}+\sqrt{50}-\sqrt{32}\right)\)
\(B=1-\left(\sqrt{45}-\sqrt{20}-\sqrt{3}\right).\left(\sqrt{20}-\sqrt{45}-\sqrt{3}\right)\)
1.\(D=\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)\(=2\sqrt{3}-10\sqrt{3}-\sqrt{3}+\frac{10\sqrt{3}}{3}\)\(=\frac{-17\sqrt{3}}{3}\)
2.\(A=27-\left(\sqrt{32}-\sqrt{50}\right)^2=25\)
\(B=1-\left(\left(-\sqrt{3}\right)^2-\left(\sqrt{20}-\sqrt{45}\right)^2\right)\)\(=1-\left(-2\right)=3\)
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thực hiện phép tính
a)\(3\sqrt{9-\sqrt{25}+2\sqrt{49}}\)
b)\(7\sqrt[3]{27}-\sqrt[3]{64}+2\sqrt[3]{8}\)
c)\(\left(\sqrt{28}+2\sqrt{14}+3\sqrt{7}\right)\left(\sqrt{7}-7\sqrt{8}\right)\)
d)\(\frac{6\sqrt{7}+\sqrt{12}}{2}+\sqrt{7}+\sqrt{67-12\sqrt{7}}\)
