If a, b are positive integers such that \sqrt{a}+\sqrt{b}=\sqrt{189}, find the value of a+b

Solve the equations involving square roots

\sqrt{x+5}+\sqrt{20-x} =7

Simplify the square root expression

\dfrac{\sqrt{2}+\sqrt{6} }{1+\sqrt{3} }

If x=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\infty}}}} , then the value of x is

Which of the following is equal to \sqrt{9-6\sqrt{2} } +\sqrt{9+6\sqrt{2} }

Prove that

\dfrac{1}{1+\sqrt{2}}+\dfrac{1}{\sqrt{2}+\sqrt{3}}+\dfrac{1}{\sqrt{3}+\sqrt{4}}+\dfrac{1}{\sqrt{4}+\sqrt{5}}+\dfrac{1}{\sqrt{5}+\sqrt{6}}+\dfrac{1}{\sqrt{6}+\sqrt{7}}+\dfrac{1}{\sqrt{7}+\sqrt{8}}+\dfrac{1}{\sqrt{8}+\sqrt{9}}=2

Simplify the radical expression

\dfrac{\sqrt{15}+\sqrt{35}+\sqrt{21}+5 }{\sqrt{3}+2\sqrt{5}+\sqrt{7} }