Bài 1: Rút gọn
a. \(\left(5-2\sqrt{3}\right)^2+\left(5+2\sqrt{3}\right)^2\)
b. \(\left(\sqrt{5}+\sqrt{2}\right)^2-\left(2\sqrt{5}+1\right)\left(2\sqrt{5}-1\right)-\sqrt{40}\)
c. \(\left(\sqrt{2}-1\right)^2-\frac{2}{3}\sqrt{4}+\frac{4\sqrt{2}}{5}+\sqrt{1\frac{11}{15}}-\sqrt{2}\)
d. \(\left(\sqrt{6}-\sqrt{18}+5\sqrt{2}-\frac{1}{2}\sqrt{8}\right)2\sqrt{6}+2\sqrt{3}\)
e. \(\left(2\sqrt{3}-3\sqrt{2}\right)^2+6\sqrt{6}+3\sqrt{24}\)
Bài 2: Rút gọn
A =\(\left(\frac{1}{x-\sqrt{x}}+\frac{1}{\sqrt{x}-1}:\frac{\sqrt{x+1}}{x-2\sqrt{x}+1}\right)\)(x>0 ; x khác 1)

Giải giúp mik vs đap cần gấp . Cảm ơn mn. Giải cho mik bài 1 cx đc

1/ Rút gọn

A=\(\sqrt{7}-4\sqrt{3}+\sqrt{4}-2\sqrt{3}\)

B=\(\left(2+\frac{5-\sqrt{5}}{\sqrt{5}-1}\right)\) \(\left(2-\frac{5+\sqrt{5}}{\sqrt{5}+1}\right)\)

C=\(\left(\sqrt{3}+1\right)\) \(\left(\frac{\sqrt{14}-6\sqrt{3}}{5+\sqrt{3}}\right)\)

2/Cho P=\(\left(\sqrt{x-\frac{1}{\sqrt{x}}}\right)\):\(\left(\frac{\sqrt{x}-1}{\sqrt{x}}+\frac{1-\sqrt{x}}{x+\sqrt{x}}\right)\)

a/ cmr: P>0, V x >0, x\(\ne\)1

b/Tính GT P khi x\(\frac{2}{2+\sqrt{3}}\)

có ai biết giải bài này không giúp mình với mình đang cần gấp, xin cảm ơn

Bài 20: rút gọn 

1, \(\sqrt{9-4\sqrt{5}}.\sqrt{9+4\sqrt{5}}\)

2, \(\left(2\sqrt{2}-6\right).\sqrt{11+6\sqrt{2}}\)

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

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

5, \(\sqrt{27+10\sqrt{2}}:\dfrac{1}{\sqrt{\left(\sqrt{2}-5\right)^2}}\)

Bài 21: rút gọn 

1, \(5\sqrt{\dfrac{1}{5}}\)                         2,  \(\dfrac{12}{5}\sqrt{\dfrac{5}{4}}\)

3, \(\dfrac{30}{5\sqrt{6}}\)                          4, \(\dfrac{20}{2\sqrt{5}}\)

5, \(\dfrac{2-\sqrt{2}}{\sqrt{2}}\)

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) \(\left(\frac{\sqrt{14}-\sqrt{7}}{1-\sqrt{2}}+\frac{\sqrt{15}-\sqrt{5}}{1-\sqrt{3}}\right):\frac{1}{\sqrt{7}-\sqrt{5}}\)

Tính:

a) \(A=\sqrt{8-2\sqrt{15}}\left(\sqrt{3}+\sqrt{5}\right)-\left(\sqrt{45}-\sqrt{20}\right)\)

b) \(B=\left(\frac{\sqrt{21}-\sqrt{3}}{\sqrt{7}-1}-\frac{\sqrt{15}-\sqrt{3}}{1-\sqrt{5}}\right)\left(\frac{1}{2}\sqrt{6}-\sqrt{\frac{3}{2}}+3\sqrt{\frac{2}{3}}\right)\)

c) \(C=2\sqrt{3}+\sqrt{7-4\sqrt{3}}+\left(\sqrt{\frac{1}{3}}-\sqrt{\frac{4}{3}+}\sqrt{3}\right):\sqrt{3}\)

d) \(D=\left(\frac{5+\sqrt{5}}{5-\sqrt{5}}+\frac{5-\sqrt{5}}{5+\sqrt{5}}\right):\frac{1}{\sqrt{7-4\sqrt{3}}}\)

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 
 

Bài 2: Thực hiện phép tính

a) \(\sqrt{5}-\sqrt{48}+5\sqrt{27}-\sqrt{45}\)

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

c) \(3\sqrt{50}-2\sqrt{75}-4\frac{\sqrt{54}}{\sqrt{3}}-3\sqrt{\frac{1}{3}}\)

d) \(\sqrt{\left(\sqrt{3}-3\right)^2}+\sqrt{4-2\sqrt{3}}\)

e) \(\sqrt{48-2\sqrt{135}}-\sqrt{45}+\sqrt{18}\)

f) \(\frac{5\sqrt{2}-2\sqrt{5}}{\sqrt{5}-\sqrt{2}}+\frac{6}{2-\sqrt{10}}-\frac{20}{\sqrt{10}}\)

Bài 3: Thực hiện phép tính

a) \(\sqrt{9-4\sqrt{5}}\)

b) \(2\sqrt{3}+\sqrt{48}-\sqrt{75}-\sqrt{243}\)

c) \(\sqrt{4+\sqrt{8}}.\sqrt{2+\sqrt{2+\sqrt{2}}}.\sqrt{2-\sqrt{2+\sqrt{2}}}\)

d) \(\sqrt{3+2\sqrt{2}}-\sqrt{6-4\sqrt{2}}\)

e) \(\frac{\sqrt{5}-\sqrt{3}}{\sqrt{5}+\sqrt{3}}+\frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}}-\frac{\sqrt{5}+1}{\sqrt{5}-1}\)

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

Bài 4: Rút gọn

a) \(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}\)

b) \(\left(2\sqrt{3}+\sqrt{4}\right)\left(\sqrt{3}-2\right)\)

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

d) \(\sqrt{4-\sqrt{15}}-\sqrt{4+\sqrt{15}}+\sqrt{6}\)

e) \(\left(\frac{5-\sqrt{5}}{\sqrt{5}}-2\right)\left(\frac{4}{1+\sqrt{5}}+4\right)\)

f) \(\frac{1}{5}\sqrt{50}-2\sqrt{96}-\frac{\sqrt{30}}{\sqrt{15}}+12\sqrt{\frac{1}{6}}\)

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