Tính Lim căn {{n^2} + 2n}  - \căn {{n^2} + n}

\(\begin{array}{l}\lim \,\left( {\sqrt {{n^2} + 2n} - \sqrt {{n^2} + n} } \right) = \lim \frac{{\left( {{n^2} + 2n} \right) - \left( {{n^2} + n} \right)}}{{\sqrt {{n^2} + 2n} + \sqrt {{n^2} + n} }}\\ = \lim \frac{n}{{n\sqrt {1 + \frac{2}{n}} + n\sqrt {1 + \frac{1}{n}} }}\\ = \lim \frac{1}{{\sqrt {1 + \frac{2}{n}} + \sqrt {1 + \frac{1}{n}} }}\\ = \frac{1}{{\sqrt {1 + 0} + \sqrt {1 + 0} }} = \frac{1}{2}\end{array}\)