\(\sqrt[3]{\left(-2^2\right)+12}\times\sqrt{576+288}\times3=???\)
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27 tháng 10 2020
a) \(\sqrt{12}-3\sqrt{75}+0,5\sqrt{\left(-6\right)^2\cdot3}\)
\(=2\sqrt{3}-15\sqrt{3}+0,5\sqrt{108}\)
\(=-13\sqrt{3}+3\sqrt{3}\)
\(=-10\sqrt{3}\)
b) \(3\sqrt{\left(\sqrt{2}-\sqrt{3}\right)^2}-\sqrt{4+2\sqrt{3}}\)
\(=3\left|\sqrt{2}-\sqrt{3}\right|-\sqrt{\left(\sqrt{3}+1\right)^2}\)
\(=3\left(\sqrt{3}-\sqrt{2}\right)-\left|\sqrt{3}+1\right|\)
\(=3\sqrt{3}-3\sqrt{2}-\sqrt{3}-1\)
\(=2\sqrt{3}-3\sqrt{2}-1\)
c) \(\left(\frac{2x+1}{x\sqrt{x}-1}-\frac{\sqrt{x}}{x+\sqrt{x}+1}\right)\div\frac{1}{x-2\sqrt{x}+1}\)
\(=\frac{2x+1-\left(\sqrt{x}-1\right)\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\div\frac{1}{\left(\sqrt{x}-1\right)^2}\)
\(=\frac{2x+1-x+\sqrt{x}}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\left(\sqrt{x}-1\right)^2\)
\(=\frac{x+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\cdot\left(\sqrt{x}-1\right)^2\)
\(=\sqrt{x}-1\)
21 tháng 7 2022
\(=\left[\left(2-\sqrt{2}\right)^2-3\right]\cdot\left(3+\sqrt{2}\right)\cdot\left(\sqrt{2}-1\right)\)
\(=\left(6-4\sqrt{2}-3\right)\left(3\sqrt{2}-3+2-\sqrt{2}\right)\)
\(=\left(3-4\sqrt{2}\right)\left(2\sqrt{2}-1\right)\)
\(=6\sqrt{2}-3-16+4\sqrt{2}=10\sqrt{2}-19\)
26 tháng 10 2020
a) \(\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{12}-\sqrt{\left(-3\right)^2}\)
\(=\left|\sqrt{3}-2\right|+\sqrt{2^2\cdot3}-\sqrt{3^2}\)
\(=2-\sqrt{3}+2\sqrt{3}-3\)
\(=\sqrt{3}-1\)
b) \(\left(\sqrt{8}-3\sqrt{6}+\sqrt{2}\right)\cdot\sqrt{2}+\sqrt{108}\)
\(=\sqrt{16}-3\sqrt{12}+\sqrt{4}+\sqrt{6^2\cdot3}\)
\(=4-3\sqrt{2^2\cdot3}+2+6\sqrt{3}\)
\(=6-3\cdot2\sqrt{3}+6\sqrt{3}\)
\(=6-6\sqrt{3}+6\sqrt{3}=6\)
NN
26 tháng 10 2020
a) \(\sqrt{\left(\sqrt{3}-2\right)^2}+\sqrt{12}-\sqrt{\left(-3\right)^2}\)
\(=\left|\sqrt{3}-2\right|+\sqrt{3.4}-\sqrt{3^2}=2-\sqrt{3}+\sqrt{4}.\sqrt{3}-3\)
\(=2-\sqrt{3}+2\sqrt{3}-3=\sqrt{3}-1\)
b) \(\left(\sqrt{8}-3\sqrt{6}+\sqrt{2}\right).\sqrt{2}+\sqrt{108}\)
\(=\sqrt{8}.\sqrt{2}-3\sqrt{6}.\sqrt{2}+\sqrt{2}.\sqrt{2}+\sqrt{108}\)
\(=\sqrt{8.2}-3\sqrt{6.2}+2+\sqrt{36.3}\)
\(=\sqrt{16}-3\sqrt{12}+2+\sqrt{36}.\sqrt{3}\)
\(=\sqrt{4^2}-3\sqrt{4.3}+2+6\sqrt{3}\)
\(=4-3\sqrt{4}.\sqrt{3}+2+6\sqrt{3}\)
\(=4-6\sqrt{3}+2+6\sqrt{3}=6\)
27 tháng 7 2023
\(=2^2+2\cdot2\cdot3\sqrt{2}+18-12\sqrt{2}\)
=4+18=22
5 tháng 10 2021
a: Ta có: \(\left(4\sqrt{2}-\dfrac{11}{2}\sqrt{8}-\dfrac{1}{3}\sqrt{288}+\sqrt{50}\right)\cdot\left(\dfrac{1}{2}\sqrt{2}\right)\)
\(=\dfrac{1}{2}\sqrt{2}\cdot\left(4\sqrt{2}-11\sqrt{2}-4\sqrt{2}+5\sqrt{2}\right)\)
\(=\dfrac{1}{2}\sqrt{2}\cdot6\sqrt{2}=3\)
HH
15 tháng 6 2018
Giải:
\(\left(\dfrac{3}{2}\sqrt{6}+2\sqrt{\dfrac{2}{3}}-4\sqrt{\dfrac{3}{2}}\right).\left(3\sqrt{\dfrac{2}{3}}-\sqrt{2}-\sqrt{6}\right).\left(-\sqrt{6}\right)\)
\(=\left(\sqrt{\dfrac{27}{2}}+\sqrt{\dfrac{8}{3}}-\sqrt{24}\right).\left(\sqrt{6}-\sqrt{2}-\sqrt{6}\right).\left(-\sqrt{6}\right)\)
\(=\left(\dfrac{\sqrt{6}}{6}\right).\left(-\sqrt{2}\right).\left(-\sqrt{6}\right)\)
\(=\sqrt{2}\)
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