Tính

a.\(\sqrt{8+2\sqrt{5}}\)     b.\(\sqrt{10-2\sqrt[]{5}}\)     c.\(\sqrt{5+\sqrt{24}}\)     d.\(\sqrt{12-\sqrt{140}}\)     

e.\(\sqrt{14+2\sqrt{5}}\)   f. \(\sqrt{8-\sqrt{28}}\)       g.\(\sqrt{23-4\sqrt{15}}\)  h.\(\sqrt{9+4\sqrt{2}}\)

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Rút gọn :

1, \(\sqrt{8}-3\sqrt{32}+\sqrt{72}\)

2, \(6\sqrt{12}-\sqrt{20}-2\sqrt{27}+\sqrt{125}\)

3 , \(3\sqrt{112}-7\sqrt{216}+4\sqrt{54}-2\sqrt{252}-3\sqrt{96}\)

4, \(3\sqrt{3}\left(3+2\sqrt{6}-\sqrt{33}\right)\)

6, \(\sqrt{2}\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)

7, \((5\sqrt{6}-4\sqrt{10}+7\sqrt{30}):\sqrt{2}\)

8, \(\left(2\sqrt{28}-3\sqrt{7}+5\sqrt{63}\right)\sqrt{112}\)

9, \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)

10, \(\left(4\sqrt{27}-2\sqrt{48}-5\sqrt{75}\right):2\sqrt{3}\)

11, \(\left(1+\sqrt{3}-\sqrt{2}\right).\left(1+\sqrt{3}+\sqrt{2}\right)\)

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Bài 1: Rút gọn biểu thức

1) \(\sqrt{12}-\sqrt{27}+\sqrt{48}\)              2) \(\left(\sqrt{25}+\sqrt{20}-\sqrt{80}\right):\sqrt{5}\)

3) \(2\sqrt{27}-\sqrt{\frac{16}{3}}-\sqrt{48}-\sqrt{8\frac{1}{3}}\)      4) \(\frac{1}{\sqrt{5}-\sqrt{3}}-\frac{1}{\sqrt{5}+\sqrt{3}}\)

5) \(\left(\sqrt{125}-\sqrt{12}-2\sqrt{5}\right)\left(3\sqrt{5}-\sqrt{3}+\sqrt{27}\right)\)   6) \(\left(3\sqrt{20}-\sqrt{125}-15\sqrt{\frac{1}{5}}\right).\sqrt{5}\)

7) \(\left(6\sqrt{128}-\frac{3}{5}\sqrt{50}+7\sqrt{8}\right):3\sqrt{2}\)  8) \(\left(2\sqrt{48}-\frac{3}{2}\sqrt{\frac{4}{3}}+\sqrt{27}\right).2\sqrt{3}\)

9) \(\sqrt{\left(3-2\sqrt{2}\right)^2}-\sqrt{\left(\sqrt{8}-4\right)^2}\)    10) \(\sqrt{\left(4-\sqrt{15}\right)^2}+\sqrt{\left(\sqrt{15}-3\right)^2}\)

11) \(\frac{\sqrt{10}-\sqrt{2}}{\sqrt{5}-1}+\frac{2-\sqrt{2}}{\sqrt{2}-1}\)      12) \(\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right)\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)

13) \(\sqrt{15-6\sqrt{6}}\)    14) \(\sqrt{8-2\sqrt{15}}\)    15) \(\sqrt[3]{-2}.\sqrt[3]{32}+\sqrt{2}.\sqrt{32}\)

Rút gọn biểu thức
I=(2\(\sqrt{3}\)-5\(\sqrt{27}\)+4\(\sqrt{12}\)):\(\sqrt{3}\)
K=\(\sqrt{125}\)-4\(\sqrt{45}\)+3\(\sqrt{20}\)-\(\sqrt{80}\)
L=2\(\sqrt{9}\)+\(\sqrt{25}\)-5\(\sqrt{4}\)
N=2\(\sqrt{32}\)-5\(\sqrt{27}\)-4\(\sqrt{8}\)+3\(\sqrt{75}\)
O=2\(\sqrt{3.5^2}\)-3\(\sqrt{3.2^2}\)+\(\sqrt{3.3^2}\)

Bài 1: Tính

1, \(A=\left(1-\frac{5+\sqrt{5}}{1+\sqrt{5}}\right).\left(\frac{5-\sqrt{5}}{1-\sqrt{5}}-1\right)\)

2, \(B=\left(\frac{3\sqrt{125}}{15}-\frac{10-4\sqrt{6}}{\sqrt{5}-2}\right).\frac{1}{\sqrt{5}}\)

3, \(C=\left(\frac{\sqrt{1000}}{100}-\frac{5\sqrt{2}-2\sqrt{5}}{2\sqrt{5}-8}\right).\frac{\sqrt{10}}{10}\)

4, \(D=\frac{1}{\sqrt{49+20\sqrt{6}}}-\frac{1}{\sqrt{49-20\sqrt{6}}}+\frac{1}{\sqrt{7-4\sqrt{3}}}\)

5, \(E=\frac{1}{\sqrt{4-2\sqrt{3}}}-\frac{1}{\sqrt{7-\sqrt{48}}}+\frac{3}{\sqrt{14-6\sqrt{5}}}\)

6, \(F=\frac{1}{\sqrt{2}-\sqrt{3}}\sqrt{\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}}\)

7, \(G=\frac{\sqrt{15-10\sqrt{2}}+\sqrt{13+4\sqrt{10}-\sqrt{11-2\sqrt{10}}}}{2\sqrt{3+2\sqrt{2}}+\sqrt{9-4\sqrt{2}+\sqrt{12+8\sqrt{2}}}}\)

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.\(10\sqrt{28}-2\sqrt{275}-3\sqrt{343}-\frac{3}{2}\sqrt{396}\)