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2 tháng 7 2019
Cách 1: 3√1728 : 3√64 = 12:4 = 3
Cách 2: 3√1728:3√64 = 3√(1728/64) = 3√27 = 3
~Học tốt~
12 tháng 2 2022
\(a=\dfrac{4\sqrt{\sqrt{5}-\sqrt{3-2\sqrt{5}+3}}}{2}\)
\(=2\sqrt{\sqrt{5}-\sqrt{5}+1}=2\)
\(P=\left(2^5-7\cdot2^2-3\right)^{81}+19=1+19=20\)
CM
4 tháng 11 2017
Cách 1: 3√1728 : 3√64 = 12:4 = 3
Cách 2: 3√1728:3√64 = 3√(1728/64) = 3√27 = 3
NN
2
TN
25 tháng 12 2019
\(=\frac{2\sqrt{2}\left(1-\sqrt{3}\right)}{3\sqrt{2-\sqrt{3}}}\)
\(=\frac{2.\left(1-\sqrt{3}\right).\sqrt{2}.\sqrt{2+\sqrt{3}}}{3.\sqrt{2-\sqrt{3}}.\sqrt{2+\sqrt{3}}}\)
\(=\frac{2.\left(1-\sqrt{3}\right).\sqrt{2\left(2+\sqrt{3}\right)}}{3.\sqrt{\left(2-\sqrt{3}\right).\left(2+\sqrt{3}\right)}}\)
\(=\frac{2.\left(1-\sqrt{3}\right).\sqrt{4+2\sqrt{3}}}{3.\sqrt{2^2-\left(\sqrt{3}\right)^2}}\)
\(=\frac{2\left(1-\sqrt{3}\right)\sqrt{\left(1+\sqrt{3}\right)^2}}{3.\sqrt{4-3}}\)
\(=\frac{2\left(1-\sqrt{3}\right)|1+\sqrt{3}|}{3\sqrt{1}}\)
\(=\frac{2\left(1-\sqrt{3}\right)\left(1+\sqrt{3}\right)}{3}\)
\(=\frac{2\left(1^2-\left(\sqrt{3}\right)^2\right)}{3}\)
\(=\frac{2.\left(-2\right)}{3}=\frac{-4}{3}\)
15 tháng 7 2019
\(a,\sqrt{\left(\sqrt{2}-3\right)^2}.\sqrt{11+6\sqrt{2}}\)
\(=|\sqrt{2}-3|.\sqrt{9+6\sqrt{2}+2}\)
\(=(3-\sqrt{2}).\left(\sqrt{\left(3+\sqrt{2}\right)^2}\right)\)
\(=\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)\)
\(=9-2=7\)
\(b,\sqrt{\left(\sqrt{3}-3\right)^2}.\sqrt{\frac{1}{3-\sqrt{3}}}\)
\(=\left(3-\sqrt{3}\right).\frac{\sqrt{1}}{\sqrt{3-\sqrt{3}}}\)
\(=\frac{3-\sqrt{3}}{\sqrt{3-\sqrt{3}}}\)
\(=\sqrt{3-\sqrt{3}}\)
\(c,-\frac{2}{3}\sqrt{\frac{\left(a-b\right)^3.b^5}{c}}.\frac{9}{4}\sqrt{\frac{c^3}{2\left(a-b\right)}}.\sqrt{98b}\)
\(=-\frac{2}{3}.\frac{\sqrt{\left(a-b\right)^3.b^5}}{\sqrt{c}}.\frac{9}{4}.\frac{\sqrt{c^3}}{\sqrt{2\left(a-b\right)}}.7\sqrt{2b}\)
\(=-\frac{2}{3}.\frac{\left(a-b\right)b^2\sqrt{\left(a-b\right)b}}{\sqrt{c}}.\frac{9}{4}.\frac{c\sqrt{c}}{\sqrt{2\left(a-b\right)}}.7\sqrt{2b}\)
\(=-\frac{2}{3}.\frac{9}{4}.7.\frac{\left(a-b\right).b^2\sqrt{\left(a-b\right)b}}{\sqrt{c}}.\frac{c\sqrt{c}}{\sqrt{2\left(a-b\right)}}.\sqrt{2b}\)
\(=-\frac{21}{2}.\left(a-b\right).b^2\sqrt{b}.c.\sqrt{b}\)
\(=\frac{-21}{2}.\left(a-b\right).b^3.c\)
\(d,\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right).2\sqrt{6}\)
\(=\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\frac{1}{2}.2\sqrt{2}\right).2\sqrt{6}\)
\(=\left(\sqrt{6}-3\sqrt{3}+5\sqrt{2}-\sqrt{2}\right).2\sqrt{6}\)
\(=\left(\sqrt{6}-3\sqrt{3}+4\sqrt{2}\right).2\sqrt{6}\)
\(=2.6-18\sqrt{2}+16\sqrt{3}\)
\(=12-18\sqrt{2}+16\sqrt{3}\)