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When you have a square root, to simplify it, take out the largest perfect square factor there is. 112 has 4 and 16 as perfect square factors, but the largest one is 16.
Then what kind of simplification are you looking for?

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Square root is the opposite of square. For example, start with a number, let's say 5. Now square it, 5^2. 5^2 means 5*5 = 25, so 5 squared equals 25. Now take the square root of 25. The square root of a number is the number than when squared gives you the number you started with. The square root of 25 is 5, because when you square 5 you get 25. You see that by taking a number, 5, then squaring it, 25, then taking the square root sqrt(25), you get back to the original number, 5. How does this help with simplifying roots? Since a numbe rmay have a factor whose square root can be taken, to simplify a square root, you need to find the factors of the number that are perfect squares whose roots are rational numbers. Example 1, simplify sqrt(4) sqrt(4) = 2 (This is a simple example) Example 2, simplify sqrt(8) 8 = 4 * 2, and we know we can take the square root of 4, so we simplify sqrt(8) like this: sqrt(8) = sqrt(4 * 2) = sqrt(4) * sqrt(2) = 2sqrt(2) So sqrt(8) = 2sqrt(2) Example 3, simplify sqrt(216) 216 = 2 * 2 * 2 * 3 * 3 * 3 = 2 * 4 * 3 * 9 = 4 * 9 * 2 * 3 = 36 * 6 sqrt(216) = sqrt(36 * 6) = 9sqrt(6)

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