How many of the numbers in the following list can be simplified? $$\sqrt2,\sqrt3,\sqrt4,\ldots,\sqrt{100}$$ For example, $\sqrt{45}=3\sqrt5$ can be simplified, but $\sqrt{30}$ cannot.
@above a LOT more can be simplified, including \sqrt9=3 and \sqrt16=4...etc
I'm also working on this problem, so this will also be a sort of notepad for me
\sqrt4=2
\sqrt8=2\sqrt2
\sqrt9=3
\sqrt12=2\sqrt3
\sqrt16=4
\sqrt18=3\sqrt2
\sqrt20=2\sqrt5
\sqrt24=2\sqrt6
\sqrt25=5
\sqrt27=3\sqrt3
\sqrt28=2\sqrt7
\sqrt32=4\sqrt2
\sqrt36=6
\sqrt40=2\sqrt10
\sqrt44=2\sqrt11
\sqrt45=3\sqrt5
\sqrt48=4\sqrt3
\sqrt49=7
\sqrt50=5\sqrt2
\sqrt52=2\sqrt13
\sqrt54=3\sqrt6
\sqrt56=2\sqrt14
\sqrt60=2sqrt15
\sqrt63=3\sqrt7
\sqrt64=8
\sqrt68=2\sqrt17
\sqrt72=6\sqrt2
\sqrt75=5\sqrt3
\sqrt76=2\sqrt19
\sqrt80=4\sqrt10
\sqrt81=9
\sqrt84=2\sqrt21
\sqrt88=2\sqrt22
\sqrt90=3\sqrt10
\sqrt92=2\sqrt23
\sqrt96=2\sqrt24
\sqrt98=7\sqrt2
\sqrt99=3\sqrt11
\sqrt100=10
I think this is completely exhaustive, because I went from numbers divisible by 4(2^2) to divisible by 9(3^2) to divisible by 25(5^2)(I skip 16 because it is 2^4 and so included already) to divisible by 49(7^2)(I skip 36 because it is (3*2)^2 and so included already) to divisible by 64(8^2), 81(9^2), and 100(10^2).
Total of 39.
