Dạng 1: Biểu thức dưới dấu căn là một số thực dương.

$$\begin{gathered} M=\sqrt{45}+\sqrt{245}-\sqrt{80} \\ =\sqrt{3^2.5}+\sqrt{7^2\cdot 5}-\sqrt{4^2.5} \\ =3\sqrt{5}+7\sqrt{5}-4\sqrt{5}=6\sqrt{5} \end{gathered}$$

$$\begin{gathered} N=5\sqrt{8}+\sqrt{50}-2\sqrt{18} \\ \begin{array}{l}=5.2\sqrt{2}+5\sqrt{2}-2.3\sqrt{2}\\ =10\sqrt{2}+5\sqrt{2}-6\sqrt{2}\\ =(10+5-6)\sqrt{2}=9\sqrt{2}\end{array} \end{gathered}$$

$$\begin{gathered} P=5\sqrt{5}-12\sqrt{5}+6\sqrt{5}-4\sqrt{5} \\ =-5\sqrt{5} \end{gathered}$$

$\begin{array}{l}A=\sqrt{12}+\sqrt{27}-\sqrt{48}\\ =2\sqrt{3}+3\sqrt{3}-4\sqrt{3}\\ =\sqrt{3}\end{array}$

$$\begin{gathered} \begin{array}{l}B=2\sqrt{3}+3\sqrt{27}-\sqrt{300}\\ =2\sqrt{3}+3\sqrt{3^2.3}-\sqrt{{10}^2.3}\end{array} \\ \begin{array}{l}=2\sqrt{3}+\mathrm{3.3.}\sqrt{3}-10\sqrt{3}\\ =\sqrt{3}\end{array} \end{gathered}$$

$\begin{array}{l}C=(2\sqrt{3}-5\sqrt{27}+4\sqrt{12}):\sqrt{3}\\ =(2\sqrt{3}-5.3\sqrt{3}+4.2\sqrt{3}):\sqrt{3}\\ =-5\sqrt{3}:\sqrt{3}=-5\end{array}$