| 13th Root |
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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 relatively easy calculation. There are 393544396177593 possibilities, in the range 2030917620904736 - 2424462017082328, for the 13th root of a 200-digit number. 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.
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