How Do You Find the Square Root of a Number?

By Staff WriterLast Updated Mar 26, 2020 8:20:33 AM ET

To find a number's square root, determine which two perfect squares the number lies between and estimate a fraction between those two perfect square roots. If it is a perfect square itself the square root can be arrived at precisely. If not, divide the number by one of the two closest square roots and average the result with the root. Round this number to two decimal places.

  1. Determine if the number is a perfect square

    To determine if the number is a perfect square, try to find a number that can be multiplied by itself to produce it. For example, 5 can be multiplied by 5 to produce 25, so 25 is a perfect square. If the number is not a perfect square, continue to the next steps.

  2. Find the closest perfect squares

    To generate a close approximation of the square root of a non-perfect square, determine which two perfect squares the number lies between. For example, if the number is 21, it lies between the perfect squares 16 and 25.

  3. Estimate the square root

    Pick one of the perfect squares that the number lies between. Divide the original number by the square root of the perfect square. Average this result with the root, and round the result off to two decimal places. Check the answer by multiplying the calculated square root by itself and determining whether this process produces the original number.