Bài 1 : Tính :

a) \(\dfrac{1}{5+2\sqrt{6}}-\dfrac{1}{5-2\sqrt{6}}\)

b) \(\sqrt{6+2\sqrt{5}}-\dfrac{\sqrt{15}-\sqrt{3}}{\sqrt{3}}\)

c) \(\dfrac{3\sqrt{2}-2\sqrt{3}}{\sqrt{3}-\sqrt{2}}:\dfrac{1}{\sqrt{16}}\)

d) \(\dfrac{3+2\sqrt{3}}{\sqrt{3}}+\dfrac{2+\sqrt{2}}{1+\sqrt{2}}-\dfrac{1}{2-\sqrt{3}}\)

e) \(\dfrac{4}{1+\sqrt{3}}-\dfrac{\sqrt{15}+\sqrt{3}}{1+\sqrt{5}}\)

f) \(\left(\dfrac{1}{2-\sqrt{5}}+\dfrac{2}{\sqrt{5}-\sqrt{3}}\right):\dfrac{1}{\sqrt{21-12\sqrt{3}}}\)

Bài 2 : Rút gọn :

a) \(\dfrac{a+b-2\sqrt{ab}}{\sqrt{a}-\sqrt{b}}:\dfrac{1}{\sqrt{a}+\sqrt{b}}\)

b) \(\left(\dfrac{\sqrt{a}}{2}-\dfrac{1}{2\sqrt{a}}\right).\left(\dfrac{a-\sqrt{a}}{\sqrt{a}+1}-\dfrac{a+\sqrt{a}}{\sqrt{a}-1}\right)\)

c) \(\left(\dfrac{1}{\sqrt{a}-1}-\dfrac{1}{\sqrt{a}}\right):\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-2}-\dfrac{\sqrt{a}+2}{\sqrt{a}-1}\right)\)

\(ab\sqrt{\dfrac{a}{b}}\)

Phân tích các đa thức sau thành nhân tử:

a) \(3-\sqrt{3}+\sqrt{15}-3\sqrt{5}\) b) \(\sqrt{1-a}+\sqrt{1-a^2}\) với -1< a <1

c) \(\sqrt{a^3}-\sqrt{b^3}+\sqrt{a^2b}-\sqrt{ab^2}\) với a > 0, b > 0

d) \(x-y+\sqrt{xy^2}-\sqrt{y^3}\) với x > 0, y > 0

\(\left(1-\sqrt{ }x\right)\left(1+\sqrt{ }x+x\right)\)

Bài 1 : Rút gọn các bt sau :

b, B=\(\dfrac{x-\sqrt{x}}{1-\sqrt{x}}\) - \(\dfrac{x\sqrt{x}}{\sqrt{x}}\)

c, C= \(\dfrac{x+2\sqrt{x}}{\sqrt{x}-x}\) - \(\dfrac{x\sqrt{x}}{\sqrt{x}+1}\)

d, D= \(\dfrac{x+2\sqrt{x}}{\sqrt{x}+2}\)+ \(\dfrac{5\sqrt{x}-2}{x-4}\) ( x> 0 ; x#4)

e, E= \(\dfrac{\sqrt{x}}{\sqrt{x}-3}\)+ \(\dfrac{\sqrt{x}-24}{x-9}\) ( x>0; x#9)

f, F= \(\dfrac{3}{\sqrt{x}+5}\) + \(\dfrac{20-2\sqrt{x}}{x-25}\)( x>0; x#25)

Mấy bạn làm giúp mk vs ... thanks trc ạ

rút gọn các biểu thức sau với x\(\ge\)0

a. \(2\sqrt{3}-4\sqrt{3x}+27-3\sqrt{3x}\)

b.\(3\sqrt{2x}-5\sqrt{8x}+7\sqrt{18x}+28\)

Tính GTBT sau: \(\dfrac{4}{\sqrt{3}+1}-\dfrac{5}{\sqrt{3}-2}+\dfrac{6}{\sqrt{3}-3}\)

Mình đang cần gấp, mai phải nộp bài rồi, ai biết thì giúp mình với! Thanks nhiều!

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

2.\(\sqrt{9-4\sqrt{5}}-\sqrt{9+\sqrt{80}}\)

3.\(\sqrt{17-12\sqrt{2}}-\sqrt{24-8\sqrt{8}}\)

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

5.\(\sqrt{8+2\sqrt{15}}-\sqrt{8-2\sqrt{15}}\)

6.\(\sqrt{17-3\sqrt{32}}+\sqrt{17+3\sqrt{32}}\)

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

Rút gọn

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

cảm ơn

Tìm ĐKXĐ của:

a) \(\sqrt{\dfrac{1}{x^2+1}}\)

b) \(\sqrt{\dfrac{-2}{x^2}}\)

Cảm ơn.