13th root

Extracting the 13th root of a number is a famous category for the mental calculation world records. The challenge consists of being given a large number (possibly over 100 digits) and asked to return the number that equals it when multiplied by itself 13 times.

Properties of the challenge

Extracting the 13th root has certain properties. One is that the 13th root of a number is much smaller: a 13th root will have approximately 1/13th the number of digits. Thus the 13th root of a 100-digit number only has 8 digits and the 13th root of a 200-digit number will have 16 digits. Further, the last digit of the 13th root is always the same as the last digit of the power.

For the 13th root of a 100-digit number there are 7992563 possibilities, in the range 41246264 - 49238826. This is considered a reatively easy calculation. The 13th root of a 200-digit number there are 393544396177593 possibilities, in the range 2030917620904736 - 2424462017082328. This is considered a difficult calculation.

Records

The Guinness Book of World Records has published records for extracting the 13th root of a 100-digit number. All world records for mentally extracting a 13th root have been for numbers with an integer root.

• The first record was 23 minutes by De Grote(Mexico).
• The most published time was 88.8 seconds by Klein(Netherlands).
• Gert Mittring seems to have calculated it in 39 seconds.
• Alexis Lemaire has broken his record with the 13.55 seconds. This is the last official world record for extracting the 13th root of a 100-digit number

External links

• The official 13th root site