Layouteditor sqrt7/14/2023 ![]() Perfect squares, on the other hand, are whole numbers that are the product of other whole numbers. For instance, 25, 36, and 49 are perfect squares because they are 5 2, 6 2, and 7 2, respectively. Perfect square factors are, as you may have guessed, factors that are also perfect squares. To start finding a square root via prime factorization, first, try to reduce your number into its perfect square factors. We want to find the square root of 400 by hand. To begin, we divide the number into perfect square factors. Since 400 is a multiple of 100, we know that it's evenly divisible by 25 - a perfect square. ![]() Quick mental division lets us know that 25 goes into 400 16 times. 16, coincidentally, is also a perfect square. Thus, the perfect square factors of 400 are 25 and 16 because 25 × 16 = 400. ![]() 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). 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 could go a little higher and multiply 10 by 10 to get 100, which is too high. You could then go a little lower and multiply 9 by 9. This would give you 81, making 9 your square root.Įstimate, if necessary. 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. One way to guide your estimates is to find the perfect squares on either side of the number in your square root. 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.
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