## sugarheart 2 years ago .

1. mathstudent55

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2. mathstudent55

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.

3. mathstudent55

Then what kind of simplification are you looking for?

4. mathstudent55

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)