Chứng minh rằng:

\(\sqrt{3.4+\dfrac{1}{5}}+\sqrt{4.5+\dfrac{1}{6}}+\sqrt{5.6+\dfrac{1}{7}}+...+\sqrt{100.101+\dfrac{1}{102}}< 5096\)

Rút gọn :

\(\left(\sqrt{2}+1\right)\left(\sqrt{3}+1\right)\left(\sqrt{6}+1\right)\left(5-2\sqrt{2}-\sqrt{3}\right)\)

Rút gọn :L=\(\sqrt{\left|40\sqrt{2}-57\right|}-\sqrt{\left|40\sqrt{2}-57\right|}\)

Rút gọn :

H=\(\dfrac{b}{a}-\dfrac{\sqrt{ab}+\sqrt{a^2}}{a}\)

Rút gọn:

K=\(\sqrt{\dfrac{1}{a^2+b^2}+\dfrac{1}{\left(a+b\right)^2}+\sqrt{\dfrac{1}{a^4}+\dfrac{1}{b^4}+\dfrac{1}{\left(a^2+b^2\right)^2}}}\)

So sánh:

a)a=\(\sqrt{2+\sqrt{3}}\) và b=\(\dfrac{\sqrt{3}+1}{\sqrt{2}}\)

b)b=\(\sqrt{5-\sqrt{13+4\sqrt{3}}}\) và c=\(\sqrt{3}-1\)

c)\(\sqrt{n+2}+\sqrt{n+1}\) và\(\sqrt{n+1}-\sqrt{n}\) (n∈N*)