Analyse and assess the positive square root of $\sqrt{50}+\sqrt{48}$

To find the positive value of  $\sqrt{50}+\sqrt{48} \to$

By taking LCM,

$2\left|50\right|$

$5\left|25\right|$

$5\left| 5 \right|$

$\left|1\right|$

50=2$\times$5$\times$5

similarly,

$2\left|48\right|$

$2\left|24\right|$

$2\left|12\right|$

$2\left| 6 \right|$

$3\left| 3 \right|$

$\left| 1 \right|$

48=2$\times$2$\times$2$\times$2$\times$3

$\Rightarrow \sqrt{50}+\sqrt{48}=\sqrt{2\times 5\times 5}+\sqrt{2\times 2\times 2\times 2\times 3}$

$=5\sqrt{2}+2\times 2\sqrt{3}$

$=5\sqrt{2}+4\sqrt{3}$

                                  $$\begin{gathered} \sqrt{2}=1.414 \\ \sqrt{3}=1.732 \end{gathered}$$

$=5\times 1.414+4\times 1.732$

$=7.07+6.928$

$\sqrt{50}+\sqrt{48}=13.998$