Question

what is the positive square root of 7+√48

Answer 1

$$\begin{gathered} \mathrm{Let}{x}^2=7+\sqrt{48} \\ \Rightarrow x=\sqrt{7+\sqrt{48}} \\ \Rightarrow x=\sqrt{4+3+4\sqrt{3}} \\ \Rightarrow x=\sqrt{{\left(2\right)}^2+{\left(\sqrt{3}\right)}^2+2\left(2\right)\left(\sqrt{3}\right)} \\ \Rightarrow x=\sqrt{{\left(2+\sqrt{3}\right)}^2} \\ \Rightarrow x=2+\sqrt{3} \end{gathered}$$