German | A Nice Olympiads Trick | No Calculator Allowed |

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[@Anonymous_MC]

nice solution

[@nasrullahhusnan2289]

Recall the famous Phytagorean triplet (3,4,5)
m²=333²+444²+555²
=555²+555²
=2(555²)
m=555sqrt(2)

[@als2cents679]

Waaaaay tooooo loooooooong
You can do it in your mind. Definitely not an Olympiads level question
m^2 = 333^2 + 444^2 + 555^2
take the 111^2 common to get
m^2 = 111^2 * ((3^2 + 4^2) + 5^2)
Now we know the famous Pythagorean triangle 3, 4, 5, so 3^2 + 4^2 = 5^2
and 5^2 + 5^2 = 2 * 5^2
Now take square root of both sides, to get
m = 111 * 5 * sqrt(2) = 555 sqrt(2)