Timeline for Converting sums of square-roots to nested square-roots
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 28, 2014 at 19:52 | comment | added | Somnium | I even failed to prove that form with 5 radicals do not exist - not enough memory. | |
| Aug 28, 2014 at 12:07 | comment | added | Oleg567 | @Somnium, yes, I think it must be huge work. Each next $a_j$ is product of $2$ in high powers. And search can be (maybe) simplified if use alternative form of nested radicals: $$\sqrt{14+\sqrt{140+\sqrt{4096+\sqrt{8847360}}}} = \sqrt{14+2\sqrt{35+4\sqrt{16+3\sqrt{15}}}},$$ $$\sqrt{32+\sqrt{672+\sqrt{229824+\sqrt{11943936000}}}} = \sqrt{32+2\sqrt{168+6\sqrt{399+60\sqrt{10}}}}.$$ | |
| Aug 28, 2014 at 8:15 | comment | added | Somnium | Just letting you know, I can prove that $3+\sqrt{2}+\sqrt{3}+\sqrt{5}$ can't be represented with 4 or less nested radicals. So I will try to find it with 8 roots, however numbers will be so big, that I don't know if my computer will find solution in reasonable time. | |
| Aug 28, 2014 at 6:33 | history | bounty awarded | Somnium | ||
| Aug 27, 2014 at 22:20 | history | answered | Oleg567 | CC BY-SA 3.0 |