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Simplying ordinary radical expressions

In simplifying radical expressions, we want to make the numbers under the radicand as simple as possible. Suppose we have the number 90 under a square root symbol. What we want to do is break up the number in such a way as to find among its factors a perfect square. 9 x 10 = 90. We've already found a perfect square: 9. The square root of 9 is 3. Once we've found the square root of this factor, we place it outside the square root symbol, to the left. Thus, we are left with a square root symbol with 10 under it and three to the left of it. We've simplified the radical expression as much as we could.

Next, let's look at the example of the square root of 50. What numbers, multiplied together, equal 50 and have a perfect square as one of their numbers? The obvious answer is 25. The square root of 25 is 5. Therefore, we place 5 to the left of the square root sign, and leave the two under it.

What about the number 300? 100 times 3 equals 300. 100 is our perfect square. The square root of 100 is 10. Therefore, we place the 10 to the left of the square root symbol, and we leave the 3 under the square root symbol. That is our answer.