a: \(=\left(8\sqrt{7}-5\sqrt{7}+6\sqrt{7}-4\sqrt{7}\right)\cdot\sqrt{7}\)
\(=5\sqrt{7}\cdot\sqrt{7}=35\)
b: \(=\left(6\sqrt{3}-12\sqrt{3}+15\sqrt{3}-8\sqrt{3}\right)\cdot\left(1-\sqrt{3}\right)=\sqrt{3}\left(1-\sqrt{3}\right)=\sqrt{3}-3\)
Rút Gọn
1.\(3\sqrt{3}+4\sqrt{12}-5\sqrt{27}\)
2.\(\sqrt{32}-\sqrt{50}+\sqrt{18}\)
3.\(\sqrt{72}+\sqrt{4\frac{1}{2}}-\sqrt{32}-\sqrt{162}\)
4.\(\left(\sqrt{325}-\sqrt{117}+2\sqrt{208}\right):\sqrt{13}\)
5.\(\left(\sqrt{12}-\sqrt{48}-\sqrt{108}-\sqrt{192}\right):2\sqrt{3}\)
6.\(\left(2\sqrt{112}-5\sqrt{7}+2\sqrt{63}-2\sqrt{28}\right)\sqrt{7}\)
7.\(\left(2\sqrt{27}-3\sqrt{48}+3\sqrt{75}-\sqrt{192}\right)\left(1-\sqrt{3}\right)\)
8.\(7\sqrt{24}-\sqrt{150}-5\sqrt{54}\)
9.\(2\sqrt{20}-\sqrt{50}+3\sqrt{80}-\sqrt{320}\)
10.\(\sqrt{32}-\sqrt{50}+\sqrt{98}-\sqrt{72}\)
11.\(3\sqrt{2}-4\sqrt{18}+2\sqrt{32}-\sqrt{50}\)
12.\(5\sqrt{48}-4\sqrt{27}-2\sqrt{75}+\sqrt{108}\)
13.\(2\sqrt{24}-2\sqrt{54}+3\sqrt{6}-\sqrt{150}\)
14.\(\sqrt{125}-2\sqrt{20}-3\sqrt{80}+4\sqrt{45}\)
15.\(2\sqrt{28}+2\sqrt{63}-3\sqrt{175}+\sqrt{112}\)
16.\(10\sqrt{28}-2\sqrt{275}-3\sqrt{343}-\frac{3}{2}\sqrt{396}\)
\(2\sqrt{8\sqrt{3}}-\sqrt{2\sqrt{3}}-\sqrt{9\sqrt{12}}\)
\(\sqrt{3}+\sqrt{7-4\sqrt{3}}\)
\(\sqrt{\left(\sqrt{7}-4\right)^2}-\sqrt{28}+\sqrt{63}\)
\(\left(15\sqrt{50}+5\sqrt{200}-3\sqrt{450}\right):\sqrt{10}\)
\(\sqrt{3}-2\sqrt{48}+3\sqrt{75}-4\sqrt{108}\)
Thực hiện các phép tính sau:
a, \(\sqrt{12}+2\sqrt{27}+3\sqrt{75}-9\sqrt{48}\)
b, \(2\sqrt{3}\cdot\left(\sqrt{27}+2\sqrt{48}-\sqrt{75}\right)\)
c, \(\left(2\sqrt{2}-\sqrt{3}\right)^2\)
d, \(\left(1+\sqrt{3}-\sqrt{2}\right)\cdot\left(1+\sqrt{3}+\sqrt{2}\right)\)
e, \(\left(\sqrt{3-\sqrt{5}}+\sqrt{3+\sqrt{5}}\right)^2\)
f, \(\left(\sqrt{\sqrt{11}+\sqrt{7}}-\sqrt{\sqrt{11}-\sqrt{7}}\right)^2\)
Tính:
\(a)D=\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\left(-\sqrt{2}\right)\\ b)2\sqrt{3}\left(\sqrt{27}+2\sqrt{48}\right)-\sqrt{75}\\ c)E=\left(\sqrt{10}+\sqrt{6}\right)\sqrt{8-2\sqrt{15}}\\ d)P=\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}}\)
\(e)M=-3\sqrt{50}+2\sqrt{98}-7\sqrt{72}\)
Rút gọn
a) \(\sqrt{75}+\sqrt{48}-\)\(\sqrt{192}\)
b)\(3\sqrt{2x}-5\sqrt{2x}-5\sqrt{2x}=9-6\sqrt{2x}\left(x>0\right)\)
c)\(3\sqrt{2x}-4\sqrt{8x}-5\sqrt{50x}\left(x>0\right)\)
d)\(\frac{1}{x^2-y^2}.\sqrt{\frac{2\left(x+y\right)^2}{3}}\left(x\ge0;y\ge0;x\ne y\right)\)
e)\(\left(3\sqrt{2}+\sqrt{3}\right).\sqrt{2}-\sqrt{54}\)
f)\(2\sqrt{21}-\left(\sqrt{28}+\sqrt{12}-\sqrt{7}\right).\sqrt{7}\)
Rút Gọn
a,\(\sqrt{75}-\sqrt{5\frac{1}{3}}+\frac{9}{2}\sqrt{2\frac{2}{3}}+2\sqrt{27}\)
b,\(\sqrt{48}+\sqrt{5\frac{1}{3}}+2\sqrt{75}-5\sqrt{1\frac{1}{3}}\)
c,\(\left(\sqrt{12}+2\sqrt{27}\right)\frac{\sqrt{3}}{2}-\sqrt{150}\)
d,\(\left(\sqrt{18}+\sqrt{0,5}-3\sqrt{\frac{1}{3}}\right)-\left(\sqrt{\frac{1}{8}-\sqrt{75}}\right)\)
e,\(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\)
f,\(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\)
g,\(\left(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\right)\sqrt{3}\)
h,\(\left(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\right)\sqrt{\frac{1}{2}}\)
i,\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)
j,\(\left(\sqrt{\frac{1}{7}}-\sqrt{\frac{16}{7}}+7\right):\sqrt{7}\)
Rút gọn
a)\(\sqrt{75}+\sqrt{75}-\)\(\sqrt{192}\)
b)3\(\sqrt{2x}-5\sqrt{2x}-5\sqrt{2x}+9-6\sqrt{2x}\left(x>0\right)\)
c)3\(\sqrt{2x}-4\sqrt{8x}-5\sqrt{50x}\left(x>0\right)\)
d)\(\frac{1}{x^2-y^2}.\sqrt{\frac{2\left(x+y\right)^2}{3}}\left(x\ge0;y\ge0;x\ne y\right)\)
e)\(\left(3\sqrt{2}+\sqrt{3}\right).\sqrt{2}\sqrt{54}\)
f)\(2\sqrt{21}-\left(\sqrt{28}+\sqrt{12}-\sqrt{7}\right).\sqrt{7}\)
1/ thực hiện phép tính :
a) \(\sqrt{200}+2\sqrt{108}-\sqrt{98}+\frac{1}{3}\sqrt{\frac{81}{3}}-3\sqrt{75}\)
b) (\(21\sqrt{\frac{1}{7}}+\frac{1}{2}\sqrt{112}-\frac{14}{3}\sqrt{\frac{9}{7}}+7\)) : \(3\sqrt{7}\)
c) \(\left(\sqrt{27}-\sqrt{125}+\sqrt{45}+\sqrt{12}\right).\left(\sqrt{75}+\sqrt{20}\right)\)
d) \(\left(\frac{3}{\sqrt{6}-3}-\frac{3}{\sqrt{6}+3}\right).\frac{3-\sqrt{3}}{2-2\sqrt{3}}-\frac{\sqrt{28-6\sqrt{3}}}{1}\)
e) \(\frac{1}{\sqrt{11}-2\sqrt{30}}-\frac{3}{\sqrt{7-2\sqrt{10}}}+\frac{4}{\sqrt{8+4\sqrt{3}}}\)
Rút gọn
1,\(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\)
2,\(\left(2\sqrt{\frac{16}{3}}-3\sqrt{\frac{1}{27}}-6\sqrt{\frac{4}{75}}\right)\sqrt{3}\)
3,\(\left(6\sqrt{\frac{8}{9}}-5\sqrt{\frac{32}{25}}+14\sqrt{\frac{18}{49}}\right)\sqrt{\frac{1}{2}}\)
4,\(\frac{1}{2}\sqrt{48}-2\sqrt{75}-\frac{\sqrt{33}}{\sqrt{11}}+5\sqrt{1\frac{1}{3}}\)
5,\(\left(\sqrt{\frac{1}{7}}-\sqrt{\frac{16}{7}}+\sqrt{7}\right):\sqrt{7}\)
Rút gọn các biểu thức sau:
a) \(\left(\sqrt{8}-3\sqrt{2}+\sqrt{10}\right)\left(\sqrt{2}-3\sqrt{0,4}\right)\) b) \(\left(\sqrt{28}-2\sqrt{14}+\sqrt{7}\right).\sqrt{7}+7\sqrt{8}\)
c) \(2\sqrt{\left(\sqrt{2}-3\right)^2}+\sqrt{2\left(-3\right)^2}-5\sqrt{\left(-1\right)^4}\) d) \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)
