How To Find the Square Root Of a Number Mentally

This method for calculating square roots works quite well with squares of whole numbers between 0 and 99.

Instructions

  • Step 1: Square the number having the same tens digit determined earlier and the number 5 as the ones digit. In the case of 1849, the square of 45 is 2025.
  • Step 2: Determine the root. If the number whose square root you are trying to determine is less than the square just calculated, then the second digit in the square root is the smaller number of the two possibilities. The number 2025 is larger than 1849, so the digit in question must be 3, and the square root is 43.
  • FACT: The world's first electronic computer, the EINIAC, used a method involving only addition and subtraction to calculate square roots.
  • TIP: If the last digit is 0 or 5, remember that the last digit in the square root is also 0 or 5.
  • Step 3: Pay attention to the last digit of the number whose square root you wish to determine. In general, there will be two possible roots that will produce that digit. In the case of the number 1849, the two digits that could produce the final digit are 3 and 7.
  • Step 4: Ignore the last two digits of the number whose square root you wish to determine. Find the number whose square is just less than the remaining number. This will be the tens digit in the square root.
  • TIP: For example, given the number 1849, note that the number 4 has a square that is just less than 18.
  • Step 5: Memorize the squares of the numbers between 1 and 9. Note that the numbers 1, 4, 6, and 9 each appear once above and below the number 5 as the final digits of the squares.

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