1. \(\sqrt{3}\) - \(2\sqrt{12}\) + \(3\sqrt{27}\) - \(4\sqrt{48}\) + \(5\sqrt{75}\)
2. \(\sqrt{175}\) - \(2\sqrt{112}\) - \(3\sqrt{63}\) - \(2\sqrt{28}\) + \(\sqrt{7}\)
3. \(3\sqrt{75}\) - \(\frac{12}{\sqrt{2}}\) - \(30\sqrt{1\frac{1}{3}}\) + \(\sqrt{75}\)
4. (\(2\sqrt{3}\) -\(\sqrt{12}\) +\(2\sqrt{27}\) ) : \(3\sqrt{3}\)
5. (\(4\sqrt{2}\) - \(\sqrt{72}\) - \(3\sqrt{50}\) ) \(\sqrt{2}\) -\(4\sqrt{25}\) + \(1\)

Bài 5> Rút gọn căn cho một số bằng phép khai phương

1> \(\sqrt{50}\) - \(\sqrt{18}\) + \(\sqrt{200}\) - \(\sqrt{162}\)

2> \(5\sqrt{5}\) + \(\sqrt{20}\) - 3\(\sqrt{45}\)

3> \(5\sqrt{48}\) - \(4\sqrt{27}\) - 2\(\sqrt{75}\) + \(\sqrt{108}\)

4> \(\dfrac{1}{2}\sqrt{48}\) - 2\(\sqrt{75}\) - \(\dfrac{\sqrt{33}}{\sqrt{11}}\) + 5\(\sqrt{1\dfrac{1}{3}}\)

5> \(3\sqrt{12}\) - 4\(\sqrt{27}\) + 5\(\sqrt{48}\)

6> \(\sqrt{12}\) + \(5\sqrt{3}\) - \(\sqrt{48}\)

7> \(3\sqrt{50}\) - 2\(\sqrt{12}\) \(\sqrt{18}\) +\(\sqrt{75}\) - \(\sqrt{8}\)

8> \(2\sqrt{75}\) - \(3\sqrt{12}\) + \(\sqrt{27}\)

1. thực hiện phép tính

a, (\(\sqrt{12}.\sqrt{75}+\sqrt{27}\)). \(\sqrt{3}\)

b, (12\(\sqrt{50}\)-8\(\sqrt{200}\)+7\(\sqrt{450}\)) : \(\sqrt{10}\)

c, (7\(\sqrt{48}\)+9\(\sqrt{27}\)-2\(\sqrt{12}\)):\(\sqrt{15}\)

d,(\(\sqrt{32}\)-\(\sqrt{50}+\sqrt{8}\)):\(\sqrt{2}\)

Bài 1 : Tìm điều kiện xác định 

a) \(\sqrt{\frac{4}{x+3}}\)
b) \(\sqrt{3x+4}\)
c) \(\sqrt{1+x^2}\)
d) \(\sqrt{\frac{3}{1-2x}}\)
Bài 2 : Rút gọn biểu thức 

1) \(5\sqrt{5}+\sqrt{20}-3\sqrt{45}\)
2) \(\sqrt{12}+\sqrt{75}-\sqrt{27}\)
3) \(\left(\sqrt{2}+2\right)\sqrt{2}-2\sqrt{2}\)
4) \(\frac{2}{4-3\sqrt{2}}-\frac{2}{4+3\sqrt{2}}\)
5) \(\left(2\sqrt{3}-3\sqrt{2}\right)^2+2\sqrt{6}+3\sqrt{24}\)
Bài 3 : Rút gọn biểu thức 

1) \(\sqrt{\left(3+\sqrt{2}\right)^2}+\sqrt{\left(3-\sqrt{2}\right)^2}\)
2) \(\sqrt{\left(2-\sqrt{3}\right)^2}-\sqrt{\left(2+\sqrt{3}\right)^2}\)
3) \(\sqrt{\left(5-3\right)^2}+\sqrt{\left(\sqrt{5}+3\right)^2}\)

Bài 4 : cho biểu thức P= \(\frac{a+4\sqrt{a}+4}{\sqrt{a}+2}+\frac{4-a}{2-\sqrt{a}}vớia\ge0;a\ne4\)

a) Rút gọn biểu thức P 
b) Tìm giá trị của a sao cho P=a+1 
 

1] rút gọn

a) (\(\sqrt{12}\) + \(3\sqrt{5}\) - \(4\sqrt{135}\)) 13

b) \(\sqrt{252}\) - \(\sqrt{700}\) + \(\sqrt{1008}\) - \(\sqrt{448}\)

c) \(2\sqrt{40\sqrt{12}}\) - \(2\sqrt{\sqrt{75}}\) -\(3\sqrt{5\sqrt{48}}\)

2]

a) A= \(\frac{\sqrt{6}+\sqrt{14}}{2\sqrt{3}+\sqrt{28}}\)

b) B= \(\frac{9\sqrt{5}+3\sqrt{27}}{\sqrt{5}+\sqrt{3}}\)

c) C= \(\frac{3\sqrt{8}-2\sqrt{12}+\sqrt{20}}{3\sqrt{18}-2\sqrt{27}+\sqrt{45}}\)

 Rút gọn các biểu thức sau :

1 )  \(\sqrt{80}\)+\(\sqrt{20}\)-\(\sqrt{5}\)-5\(\sqrt{45}\)

2 ) 4\(\sqrt{20}\)-3\(\sqrt{125}\)+5\(\sqrt{45}\)-15\(\sqrt{\frac{1}{5}}\)

3 ) (7\(\sqrt{48}\)+3\(\sqrt{27}\)-2\(\sqrt{12}\)) :\(\sqrt{3}\)

4 ) \(\sqrt{343a}\)+\(\sqrt{63a}\)-\(\sqrt{28a}\)\(\left(a\ge0\right)\)

5 ) -\(\sqrt{36a}\)-\(\frac{1}{3}\).\(\sqrt{54a}\)+\(\frac{1}{5}\).\(\sqrt{150a}\)\(\left(a\ge0\right)\)

6 ) \(2\)\(\sqrt{48}\) -\(4\)\(\sqrt{27}\)+\(\sqrt{75}\)+\(\sqrt{12}\)

Rút gọn biểu thức 
1)\(\frac{15}{3\sqrt{20}}\)
2) \(\frac{\sqrt{15}-\sqrt{6}}{\sqrt{2}-\sqrt{5}}\)
3) \(\frac{3}{\sqrt{5}-\sqrt{2}}+\frac{4}{\sqrt{6}+\sqrt{2}}\)
4) \(\sqrt{\frac{3}{20}}+\sqrt{\frac{1}{60}}-2\sqrt{\frac{1}{15}}\)
5) \(\left(\sqrt{20}-\sqrt{45}+\sqrt{5}\right)\sqrt{5}\)
6)\(\left(2+\sqrt{5}\right)^2-\left(2+\sqrt{5}\right)^2\)
7) \(\left(5\sqrt{\frac{1}{5}}+\frac{1}{2}\sqrt{20}-\frac{5}{4}\sqrt{\frac{4}{5}+\sqrt{5}}\right):2\sqrt{5}\)
8)\(\frac{1}{3}\sqrt{48}+3\sqrt{75}-\sqrt{27}-10\sqrt{1\frac{1}{3}}\)
9) \(2\sqrt{3}\left(2\sqrt{6}-\sqrt{3}+1\right)\)
10) \(\left(5\sqrt{3}+3\sqrt{5}\right):\sqrt{15}\)
11) \(\sqrt{\sqrt{10}+1}.\sqrt{\sqrt{10}-1}\)
12) \(\frac{5\sqrt{7}-7\sqrt{5}+2\sqrt{70}}{\sqrt{35}}\)
13) \(\sqrt{\frac{3}{4}}+\sqrt{\frac{1}{3}}+\sqrt{\frac{1}{12}}\)
14) \(\left(\sqrt{\frac{2}{3}}+\sqrt{\frac{3}{2}}\right)\sqrt{6}\)
15 ) \(\sqrt{\frac{4}{3}}+\sqrt{12}-\frac{4}{3}\sqrt{\frac{3}{4}}\)
16) \(\frac{1}{\sqrt{5}+\sqrt{3}}-\frac{1}{\sqrt{5}-\sqrt{3}}\)
17) \(\frac{1}{2+\sqrt{3}}+\frac{\sqrt{2}}{\sqrt{6}}-\frac{2}{3+\sqrt{3}}\)

Rút gọn:
a. \(\sqrt{7+4\sqrt{3}}\)
b.\(\sqrt{13-4\sqrt{3}}\)
c.\(\sqrt{5-2\sqrt{6}}\)
d.\(\sqrt{3+2\sqrt{2}+\sqrt{6-4\sqrt{2}}}\)
e.\(2+\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
f.\(\sqrt{3a}.\sqrt{12a}\)với a < 0
g.\(\sqrt{16a^2b^8}\)
h.\(\sqrt{7a}.\sqrt{63a^3}\)với a > 0
i.\(\sqrt{2,7a}.\sqrt{5a^3}.\sqrt{1,5a^2}\)vớ a > 0

Rút gọn:
a. \(\sqrt{7+4\sqrt{3}}\)
b.\(\sqrt{13-4\sqrt{3}}\)
c.\(\sqrt{5-2\sqrt{6}}\)
d.\(\sqrt{3+2\sqrt{2}+\sqrt{6-4\sqrt{2}}}\)
e.\(2+\sqrt{17-4\sqrt{9+4\sqrt{5}}}\)
f.\(\sqrt{3a}.\sqrt{12a}\)với a < 0
g.\(\sqrt{16a^2b^8}\)
h.\(\sqrt{7a}.\sqrt{63a^3}\)với a > 0
i.\(\sqrt{2,7a}.\sqrt{5a^3}.\sqrt{1,5a^2}\)vớ a > 0

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