Tính thu gọn :

a , \(\sqrt{17-12\sqrt{2}}-\sqrt{17+12\sqrt{2}}\)

b , \(\sqrt{27+12\sqrt{5}}-\sqrt{27-12\sqrt{5}}\)

c , \(\sqrt{15-6\sqrt{6}}+\sqrt{15+\sqrt{6\sqrt{6}}}\)

d , \(\sqrt{4+\sqrt{15}}+\sqrt{4-\sqrt{15}}-2\sqrt{3-\sqrt{5}}\)

e , \(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)

f , \(\sqrt{5+\sqrt{3-\sqrt{29-12\sqrt{5}}}}\)

thực hiện phép tính

a)\(\sqrt{6+2\sqrt{5}}-\sqrt{62\sqrt{5}}\)

b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9-4\sqrt{5}}\)

c) \(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)

d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{ }5}\)

e)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)

f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)

g) \(\sqrt{43+24\sqrt{3}}-\sqrt{49-8\sqrt{3}}\)

1. \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{8}\)

2. \(\dfrac{\sqrt{3-2\sqrt{3}}}{\sqrt{17-12\sqrt{2}}}-\dfrac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)

3.\(\sqrt{7+2\sqrt{6}}-\sqrt{\left(\sqrt{6-1}\right)^2}\)

4\(\sqrt{5-2\sqrt{6}}-\sqrt{5+\sqrt{24}}\)

5.\(\sqrt{4\sqrt{5+\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}}\)

6.\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

1. \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{8}\)

2. \(\dfrac{\sqrt{3-2\sqrt{3}}}{\sqrt{17-12\sqrt{2}}}-\dfrac{\sqrt{3+2\sqrt{2}}}{\sqrt{17+12\sqrt{2}}}\)

3.\(\sqrt{7+2\sqrt{6}}-\sqrt{\left(\sqrt{6}-1\right)^2}\)

4\(\sqrt{5-2\sqrt{6}}-\sqrt{5+\sqrt{24}}\)

5.\(\sqrt{4\sqrt{5+\sqrt{3+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}}}\)

6.\(\sqrt{6+2\sqrt{5-\sqrt{13+\sqrt{48}}}}\)

Thực hiện phép tính:

a) \(\sqrt{6+2\sqrt{5}}-\sqrt{6-2\sqrt{5}}\)

b)\(\sqrt{24-8\sqrt{5}}+\sqrt{9+4\sqrt{5}}\)

c)\(\sqrt{6-4\sqrt{2}}+\sqrt{22-12\sqrt{2}}\)

d)\(\sqrt{41+12\sqrt{5}}-\sqrt{46-6\sqrt{5}}\)

e)\(\sqrt{7+4\sqrt{3}}-\sqrt{7-4\sqrt{3}}\)

f)\(\sqrt{17-12\sqrt{2}}+\sqrt{9+4\sqrt{2}}\)

g)\(\sqrt{43+24\sqrt{3}}-\sqrt{49-\sqrt{8\sqrt{3}}}\)

h)\(\sqrt{53-20\sqrt{7}}-\sqrt{64+6\sqrt{7}}\)

Tính

1) \(\sqrt{18}.\sqrt{2}\)

2) \(\sqrt{15^2-9^2}\)

3) \(\sqrt{46-6\sqrt{5}}-\sqrt{46+6\sqrt{5}}\)

4)\(\sqrt{21+6\sqrt{6}}-\sqrt{21-6\sqrt{6}}\)

5) \(\left(2+\sqrt{5}\right).\sqrt{9-4\sqrt{5}}\)

6)\(\left(3-\sqrt{2}\right).\sqrt{7+4\sqrt{3}}\)

7)\(\left(\sqrt{3}+\sqrt{5}\right).\sqrt{7-2\sqrt{10}}\)

8)\(\left(\sqrt{6}+\sqrt{10}\right).\sqrt{4-\sqrt{15}}\)

9) \(\sqrt{2}.\left(\sqrt{8}-\sqrt{32}+3\sqrt{18}\right)\)

10) \(\sqrt{2}\left(\sqrt{2}-\sqrt{3-\sqrt{5}}\right)\)

11) \(\sqrt{3}-\sqrt{2}-\sqrt{\left(\sqrt{3}+\sqrt{2}\right)^2}\)

12) \(\left(\sqrt{2}-\sqrt{3+\sqrt{5}}\right).\sqrt{2}+2\sqrt{5}\)

tính : \(a,\sqrt{3-4\sqrt{\text{5}}}-\sqrt{9+\sqrt{30}}\)                                    l,\(\sqrt{31-8\sqrt{1\text{5}}}+\sqrt{24-6\sqrt{1\text{5}}}\)

b,\(\sqrt{17-12\sqrt{2}}-\sqrt{24-8\sqrt{8}}\)                            m,\(\sqrt{49-\text{5}\sqrt{96}}-\sqrt{49+\text{5}\sqrt{96}}\)

\(c,\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)                                 n, \(\sqrt{3+2\sqrt{2}}+\sqrt{\text{5}-2\sqrt{4}}\)

d,\(\sqrt{8+2\sqrt{1\text{5}}}-\sqrt{8-2\sqrt{1\text{5}}}\)

 f,\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)

g,\(\sqrt{6+2\sqrt{\text{5}}}+\sqrt{6-2\sqrt{\text{5}}}\)

h,\(\sqrt{11+6\sqrt{2}}-\sqrt{11-6\sqrt{2}}\)

k,\(\sqrt{1\text{5}-6\sqrt{6}}+\sqrt{33-12\sqrt{6}}\)       

Bài 1: Tính

A=\(\sqrt{46-6\sqrt{5}}-\sqrt{29-12\sqrt{5}}\)

B=\(\sqrt{13-\sqrt{160}-\sqrt{53+4\sqrt{90}}}\)

C=\(\sqrt{15-6\sqrt{6}}+\sqrt{35-12\sqrt{6}}\)

D=\(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)

E= \(\sqrt{4-\sqrt{7}}+\sqrt{4+\sqrt{7}}\)

F= \(\sqrt{3+\sqrt{11+6\sqrt{2}}}-\sqrt{5+2\sqrt{6}}\)

G=\(\sqrt{5\sqrt{3}+5\sqrt{48-10\sqrt{7+4\sqrt{3}}}}\)

Bài 2: so sánh

a) \(\sqrt{24}+\sqrt{45}\)  và 12

b) \(\sqrt{37}-\sqrt{15}\)  và 2

c) \(\sqrt{16}\) và \(\sqrt{15}\times\sqrt{17}\)

d) 8 và \(\sqrt{15}+\sqrt{17}\)

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) \(\sqrt[3]{-2}.\sqrt[3]{32}+\sqrt{2}.\sqrt{32}\)