Ever seen a 200 digit number? For those who haven't, here's one:
85,877,066,894,718,045,602,549,144,850,158,599,202,771,247,748,960,878,023,151,390,314,284,284,465,842,798,373,290,242,826,571,823,153,045,030,300,932,591,615,405,929,429,773,640,895,967,991,430,381,763,526,613,357,308,674,592,650,724,521,841,103,664,923,661,204,223Imagine being given that number and then being asked to find a number that, when multiplied by itself 13 times, will give that number as an answer (in other words, the 13th root). Oh, and you have less than 90 seconds!
That was the task set for Alexis Lemaire on July 24th of this year, and he did it in only 77.99 seconds at Oxford's Museum of the History of Science!
Back in 2004, Lemaire also set a record for finding the 13th root of a 100-digit number in only 3.62 seconds!
How does someone even begin to calculate a 13th root? The best way is to work up to the task slowly. The best place to start is to learn how to do cube roots. This gives you an idea of some of the processes and abilities needed to perform mental root calculations.
From there, you can work up to fifth roots, and then to square roots. Yes, it is strange that square roots are trickier to mentally calculate than 3rd or 5th roots, but that is indeed the case.
Once you're familiar with those, you can start working on 13th roots themselves. A knowledge and understanding of logarithms will be of great help here.
In case you've been wondering, I'll wrap up by ending the suspense. The 13th root of the aforementioned 200-digit number is 2396232838850303.