You'll know that the decimal value of the number in your square root is somewhere between these two numbers, so you'll be able to guess in between them.
One way to guide your estimates is to find the perfect squares on either side of the number in your square root. With your square root in simplest terms, it's usually fairly easy to get a rough estimate of a numerical answer by guessing the value of any remaining square roots and multiplying through. This would give you 81, making 9 your square root.Įstimate, if necessary. You could then go a little lower and multiply 9 by 9. You could go a little higher and multiply 10 by 10 to get 100, which is too high. Let's say you were trying to find the square root of 81-you could multiply 7 by 7 to get 49, which is too low.
You can also try multiplying different numbers by themselves and see if they give you the correct answer. We would write this as: Sqrt(400) = Sqrt(25 × 16). Thus, the perfect square factors of 400 are 25 and 16 because 25 × 16 = 400. 16, coincidentally, is also a perfect square. Quick mental division lets us know that 25 goes into 400 16 times. Since 400 is a multiple of 100, we know that it's evenly divisible by 25 - a perfect square. To begin, we divide the number into perfect square factors. We want to find the square root of 400 by hand. To start finding a square root via prime factorization, first, try to reduce your number into its perfect square factors. Perfect square factors are, as you may have guessed, factors that are also perfect squares. For instance, 25, 36, and 49 are perfect squares because they are 5 2, 6 2, and 7 2, respectively. Perfect squares, on the other hand, are whole numbers that are the product of other whole numbers. X Research source For instance, you could say that the factors of 8 are 2 and 4 because 2 × 4 = 8. A number's factors are any set of other numbers that multiply together to make it. 
This method uses a number's factors to find a number's square root (depending on the number, this can be an exact numerical answer or a close estimate). Divide your number into perfect square factors.
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