Though it's not essential, you may find that it's easiest to perform this process if you visually organize your workspace and your number into workable chunks. This method uses a process similar to long division to find an exact square root digit-by-digit. Separate your number's digits into pairs. From here, we can estimate Sqrt(2) and Sqrt(11) and find an approximate answer if we wish. = Our square root in simplest terms is (2) Sqrt(2 × 11) or (2) Sqrt(2) Sqrt(11).Since 2 is a prime number, we can remove a pair and put one outside the square root. As one final example problem, let's try to find the square root of 88:.Simply remove the 3's and put one 3 outside the square root to get your square root in simplest terms: (3)Sqrt(5). Thus, we can write our square root in terms of its factors like this: Sqrt(3 × 3 × 5). We know that 45 = 9 × 5 and we know that 9 = 3 × 3. As an example, let's find the square root of 45 using this method.When you find two prime factors that match, remove both these numbers from the square root and place one of these numbers outside the square root. Then, look for matching pairs of prime numbers among your factors. Write your number out in terms of its lowest common factors. Finding perfect square factors isn't necessary if you can easily determine a number's prime factors (factors that are also prime numbers). Reduce your number to its lowest common factors as a first step. Checking with a calculator gives us an answer of about 5.92 - we were right. Since 35 is just one away from 36, we can say with confidence that its square root is just lower than 6. 35 is between 25 and 36, so its square root must be between 5 and 6. For example, Sqrt(35) can be estimated to be between 5 and 6 (probably very close to 6).
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