- 1). Start by factoring the number under the radical, known as the radicand, into a product of primes. If you are solving sqrt(75), you will factor 75 to 3 * 5 * 5. Write this under the radical: sqrt(3 * 5 * 5).
- 2). Find duplicate numbers. In this example, there are two 5s. For every two factors you can take one out from under the radical when you are simplifying square roots. So in this example, you will take out a 5 for the two that are under the radical. This looks like 5 sqrt(3).
- 3). Because there is only one 3 under the radical, you cannot take any out. 5 sqrt(3) is the final answer.
- 4). Do the same thing when you have a variable. If you are solving sqrt(32 x^2 y^7) you will start by factoring the 32. This gives you sqrt(2 * 2 * 2 * 2 * 2 * x^2 y^7).
- 5). Write out the variables without exponents. This gives you sqrt(2 * 2 * 2 * 2 * 2 * x * x * y * y * y * y * y * y * y).
- 6). Take out a factor for every pair that you see under the radical. This will mean that you will take out two 2s, one x, and three y's. Leave the leftover factors under the variable: 2 * 2 * x * y * y sqrt (2y).
- 7). Multiply the factors that you brought out from under the radical. This gives you 4xy^2 sqrt (2y). This is the final answer.
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