# How to Simplify Radicals

## Simplifying Radicals

Many times, the radicand, or the number under the square root sign, isn’t a perfect square, but you can still simplify the expression If it contains a perfect square. Let’s look at three examples. We’re going to use this rule that the square root of AB is equal to the square root of A times the square root of B. We’re going to break down our numbers. 75 is not a perfect square, but it does contain a perfect square. 75 is 25 times 3.

I’m going to rewrite the square root of 75 as the square root of 25 times 3. 25 is a perfect square. Now I can use this rule that the square root of A times B is equal to the square root of A times the square root of B. I’m going to rewrite this as the square root of 25 times the square root of 3. Now that I’ve broken it up, I can actually take the square root of 25. The square root of 25 is 5 times the square root of 3. Five square roots of 3.

The square root of 25 in simplest radical form would be five square roots of 3. Let’s look at the square root of 18. Again, 18 is not a perfect square, but it does contain a perfect square. I could rewrite the square root of 18 as the square root of 9 times 2. 9 is a perfect square. I’m going to use my rule again and I’m going to write it as the square root of 9 times the square root of 2. Now I can take the square root of my perfect square

The square root of 9 is 3, and 3 times the square and of 2 is simply three square roots of 2. Last one. The square root of 600. Again, 600 is not a perfect square, but it does contain a perfect square. I’ll rewrite this as the square root of 100 times 6, 6 being our perfect square. Then I can use my rule again and write it as the square root of 100 times the square root of 6. We can take the square root of 100. The square root of 100 is 10, since 10 times 10 is 100, times the square root of six ten square roots six.