Mental Calculation Records: Extracting Roots


The records in this list are "standard calculation tasks". Record breakers should try to break one of the records in our list instead of creating new categories. It is very unlikely that new categories will be added to our lists.

If you are going to break one of these records, please contact us.

Calculating the Square Root of a Six-Digit Number

The Rules

This record is for the fastest time for an individual to calculate the square roots of ten six-digit number to eight significant numbers without a single error. The general rules for calculating records and the specific rules for the square root category at the Mental Calculation World Cup apply.

The Records

7:37 min
Selçuk Soner Akgül (Turkey) 6 September 2009 Memoriad Turkey in Ankara
6:37 min
Hakan Gürbaşlar (Turkey)
20 March 2010
Middle East Technical University in Ankara
6:19 min
Selçuk Soner Akgül (Turkey) 2 June 2010
Nermin Mehmet Çekiç Anadolu Lisesi, Ankara
4:55 min
Hakan Gürbaşlar (Turkey) 17 December 2011
Ankara VIDEO
2:43 min Priyanshi Somani (India) 3 January 2012
Lourdes Covent School in Surat, India
2:06.8 min Rhea Sandeep Shah (India) 31 August 2013
Turkish Memoriad, Ankara
1:33.8 min Rhea Sandeep Shah (India) 31 August 2013 Turkish Memoriad, Ankara
1:30.0 min Rhea Sandeep Shah (India) 31 August 2013 Turkish Memoriad, Ankara
1:07.5 min Granth Rakesh Thakkar (India) 2 September 2013
Memoriad Center, Ankara
1:04.9 min
Granth Rakesh Thakkar (India) 7 October 2014
1:01.9 min
Granth Rakesh Thakkar (India) 7 October 2014
0:47.7 min
Granth Rakesh Thakkar (India) 16 July 2022
Mental Calculation World Cup in Paderborn (Germany)

Additional statistics and national records can be found in the mental calculation world ranking list.

13th root of a 100 digit number

The Rules

[Note: In future, no more records for single tasks will be considered. The record category will be replaced with new records for the fastest time to solve 9 tasks or 3 tasks (see below)]

The general rules for calculating records apply.
  1. The record is a standard test of straightforward mental calculation for high order integer roots. The calculator should perform the calculation in his/her head without the aid of any other person and without using a calculating machines, computers, etc. nor may the calculator write down any intermediate results which are not part of the final result.
  2. The numbers of 100 digits whose 13th root is to be calculated should be randomly selected by computer immediately prior to the calculation.  It is important that the given numbers are the 13th power of integer numbers between 41246264 and 49238826, both inclusive. They should be displayed to the calculator on a computer screen, board, sheet of paper, screen or similar.
  3. The calculator has to write down the answers.
  4. The timing begins when the number becomes visible to the competitor and ends at the end of writing the answer.
  5. In some cases, the calculator may dictate the answers - then the timing ends as the calculator finishes dictating the last result.
  6. Two stop watches should be used: it would be appreciated these stopwatches record in minutes and seconds and tenths of a second rather than hundredths of an hour. At the end of the attempt the time should be taken as an average of the two watches.The name of the person making the attempt should be given, along with the date and place.
Willem Klein (Netherlands) improved his record for a single task five times - from 322 seconds in 1975 to finally 88.8 seconds in 1981. Later both Gert Mittring (Germany) and Alexis Lemaire (France) solved a single task in less than 15 seconds. Because the difficulty of the problem depends on the 100-digit number, no more records for solving a single task will be considered.
Wim Klein (GIF, 7 kB)

Wim Klein

Gert Mittring (JPG, 9 kB)

Gert Mittring

23rd root of a 200 digit number

(The 200 digit number should be a number raised to the 23rd power.)

 50   sec Shakuntala Devi (India)          1977      Dallas
In 2002, Gert Mittring calculated the 23rd root of a 200 digit number in 40.83 seconds. While the attempt was not officially verified, there is no doubt that he has done the calculation in this time.
No more records for this category will be considered.

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