physics - How to get to this result? $sqrt{frac{2times6.73times10^{-19}}{9.109times10^{-31}}}=sqrt{1.50times 10^{12}}$

I'm sorry but I can't understand what's happening between

$$\sqrt{\frac{2\times6.73\times10^{-19}}{9.109\times10^{-31}}}=\sqrt{1.50\times 10^{12}}$$ This is what the solutions from my manual have written on them, but I don't get how that operation was done. Thanks in advance

Answer

We have $6.73 = 673\times 10^{-2}$ and $9.107=9107\times 10^{-3}$ and recall that $10^a\times 10^b=10^{a+b}$ for $a,b\in\mathbb{R}$.

So, we get the following

$$\sqrt{\frac{2\times 673\times 10^{-2}\times 10^{-19}}{9107\times 10^{-3}\times 10^{-31}}}= \sqrt{\frac{2\times 673\times 10^{-21}}{9107\times 10^{-34}}}= \sqrt{\frac{2\times 673\times 10^{34} \times 10^{-21}}{9107}}=\sqrt{0.1477\times 10^{13}}$$

which leads to approximately $\sqrt{1.5\times 10^{12}}$ since $\frac{2\times 673}{9107}=0.1477\approx 0.15$.