Tìm điều kiện để các biểu thức sau xác định

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

b)\(2.\sqrt{1-2x}-\dfrac{\sqrt{3}-1}{4}\)

c)\(\sqrt{x+1}-\sqrt{x-2}\)

d)\(\sqrt{2-3x}-\sqrt{1-2x}\)  

e)\(2.\sqrt{\sqrt{3}-2x}+\dfrac{1}{x-1}\)

f)\(\dfrac{1}{2}.\sqrt{x-\dfrac{\sqrt{3}}{2}}-\dfrac{1}{\sqrt{x}-1}\)

g)\(\dfrac{1}{\sqrt{x}-1}-\dfrac{1}{\sqrt{x}+2}\)

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

Tìm x 

a)\(\sqrt{2x-1}=3\)

b)\(\sqrt{1-3x}=\dfrac{1}{2}\)

c)\(\sqrt{\left(x-1\right)^2}=\dfrac{1}{2}\)

d)\(\sqrt{\left(1+2x\right)^2}=\dfrac{\sqrt{3}}{2}\)

e)\(\sqrt{\left(1-2x\right)^2=|x-1|}\)

Thực hiện phép tính

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

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

c)\(4.\sqrt{\left(2-\dfrac{\sqrt{3}}{2}\right)^2}-3.\sqrt{\left(\sqrt{3}-1\right)^2}\)

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

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

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

Tìm x

a)\(2\sqrt{2}-\dfrac{1}{2}.\sqrt{x}=0\)

b)\(2.\sqrt{x}-\sqrt{\dfrac{x}{3}}=1\)

c)\(4.\sqrt{x}+\sqrt{\dfrac{x}{2}}=\dfrac{1}{3}\)

Tìm x

a)\(\sqrt{x-1}=2\left(x\ge1\right)\)

b)\(\sqrt{3-x}=4\left(x\le3\right)\)

c)\(2.\sqrt{3-2x}=\dfrac{1}{2}\left(x\le\dfrac{3}{2}\right)\)

d)\(4-\sqrt{x-1}=\dfrac{1}{2}\left(x\ge1\right)\)

e)\(\sqrt{x-1}-3=1\)

f)\(\dfrac{1}{2}-2.\sqrt{x+2}=\dfrac{1}{4}\)

So sánh

a)2.\(\sqrt{5}\) và 5

b)\(\dfrac{1}{3}.\sqrt{16}\) và \(\sqrt{12}\)