1h video, so I won't watch it right now. (I do recommend people to do it though - from quick glances she's rather didactic.)
That said, the radius depends on what you're looking for, and odds are that her video explains this:
If you're dealing with an isolated hydrogen atom, and you want to be bloody 100% sure that you got it full (electron and nucleus), then the radius is infinite. Because that's how wave functions work, even if the nucleus is here there's a non-zero chance that the electron is in the Moon.
If "infinite" is too much you can't be picky. You can use a₀ instead (Bohr radius), that is the most probable distance between the electron and the nucleus. Then the radius is 53pm, it's the distance that she mentions in the video description.
There are other ways to do this if you're accepting that your atom is not isolated. You could use the covalent radius instead, measuring the distance between two hydrogen nuclei in a H₂ and dividing it by two. You'll get 25±5pm; smaller than the above because they share the electrons, so it's like the atoms overlap.
Then there's the Van der Waals radius; it's a bit of a silly simplification, where you pretend that the atoms are dense, tightly packed, and non-overlapping spheres at 0°K. Then from the resulting volume you get the radius of each atom, for hydrogen it's 109pm. (This "let's pretend" stuff might sound weird, and it is, but it's still useful to know the volume of the gas more precisely than the equation pV = nRT would allow you to.)
