The 13th Root of a 200-Digit Number. In Your Head. Starting... now!

On April 6th, 2005, Alexis Lemaire from France became the first human to calculate mentally the 13th root of a 200-digit number. He took 742 attempts and 513.55 seconds, exactly 500 seconds more than his first world record in 13.55 seconds with 100 digits.

83689566882369569398373286622256452247267804664938
36677497357558157303507570408962528802385783156837
68029349382010563433638555959315144504151494907094
19097704449305660268402771869624155688082648640933

His correct answer was 2391481494636373.

I know exactly what you're thinking: 742 attempts? HOW LAME!

Yeah, I know, it's the last three digits that are the hardest. I was like all totally 2391481494636378, too. Feeling your pain.