Tính \(S=\dfrac{4+\sqrt{3}}{1+\sqrt{3}}+\dfrac{6+\sqrt{8}}{\sqrt{3}+\sqrt{5}}+...+\dfrac{240+\sqrt{14399}}{\sqrt{119}+\sqrt{121}}\)

a 

\(\sqrt{25-3\sqrt{\frac{4}{3}}}\)

b\(\left(-2^3\right)+\frac{1}{2}:\frac{1}{8}-\sqrt{25}+\left|-64\right|\)

c\(\left(-2^2\right)+\sqrt{36}.2-\sqrt{9}.3+\sqrt{25}\)

Tính giá trị các biểu thức: 

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

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

Tính nhanh : \(\frac{1}{\sqrt{1}+\sqrt{2}}+\frac{1}{\sqrt[1]{2}+\sqrt[2]{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+\frac{1}{\sqrt[3]{4}+\sqrt[4]{5}}+...+\frac{1}{\sqrt{999}+\sqrt{1000}}+\frac{1}{\sqrt[999]{1000}+\sqrt[1000]{1001}}\)

So sánh 45 với S, biết:

S= \(\frac{1}{\sqrt{1}}\)+ \(\frac{1}{\sqrt{2}-\sqrt{1}}\)+ \(\frac{1}{\sqrt{3}-\sqrt{2}}\)+ \(\frac{1}{\sqrt{4}-\sqrt{3}}\)+....+ \(\frac{1}{\sqrt{2025}-\sqrt{2024}}\)

Tính \(A=\frac{1}{2.\sqrt{1}+1.\sqrt{2}}+\frac{1}{3\sqrt{2}+2\sqrt{3}}+\frac{1}{4\sqrt{3}+3\sqrt{4}}+....+\frac{1}{100.\sqrt{99}+99.\sqrt{100}}\)

tìm gtln hoặc gtnn: a,p= 3.|2x-y|+2\(\sqrt{x-3}\) b,n=-4\(\sqrt{6}\) -3x-7 c,h=4(x-2y)\(^8\) = 2\(\sqrt{y+2+3}\) d,s= ,\(\dfrac{-7}{3\sqrt{ }x-4+2\left(x-3y^{ }\right)^{ }4+2}+3\)

So sánh

a) 3*\(\sqrt{2}\) và 7, (21)

b) \(\frac{1}{\sqrt{1}+\sqrt{2}}\) + \(\frac{1}{\sqrt{2}+\sqrt{3}}+\frac{1}{\sqrt{3}+\sqrt{4}}+.....+\frac{1}{\sqrt{99}+\sqrt{100}}\) và 9

Thực hiện phép tính (tính nhanh nếu có thể):

4) \(4\cdot\left(\dfrac{-1}{2}\right)^3+\left|-1\dfrac{1}{2}+\sqrt{\dfrac{9}{4}}\right|:\sqrt{25}\)

5) \(\left[6-3\cdot\left(\dfrac{-1}{3}\right)^2+\sqrt{\dfrac{1}{4}}\right]:\sqrt{0,\left(9\right)}\)