1. Simplify Radicals and Operations with Radicals Made Easy
By Taylor Sablowsky

2. What is it?
When you have √4, it simplifies to 2, because it is a perfect square.
When you have √24 though, it’s not a perfect square, so you have some work to do.
Even though 24 is not a perfect square, it can be broken down into smaller pieces where one of those pieces might be perfect square.
Ex:√24=√6 x √4=2√6

3. Detailed Example
√54
First you find a perfect square that goes into 54, like 9. So you have √9 x √6
Now, You take the perfect square, “9” and find it’s square root, “3”, and you put that on the outside of the “√”
This gives you 3√6, which is just √54 simplified, and your answer!

4. Examples
3√320, when there is a “3”, on the “√” you must find a perfect cube that goes into the #, in this case it would be 64 (4cubed)x 5. So you take the cube, which is 4, and put it on the outside, which makes your answer 43√5
When you have variables, like √16a2b4, you simply divide each by two, and bring them outside the “√”. So your answer would be “4ab2”

5. More Examples
√18x5y4z
The perfect square for 18 is “9” which is “3” squared, x5 cannot be divided by 2, so you leave one x behind, giving you x4+x, which lets you bring x2 outside the “√”. Y4 is divided by 2, letting you bring “y2” outside. Z is only one, so you must leave it inside. This gives you..
3x2y2√2xz

6. Now You Try
√27
√72x4
√75x3y5
√14x
√128x16
BONUS: √340x5y9z7

7. Helpful Hints Memorize your perfect squares:
4,9,16,25,36,49,64,81,100,121,144
Try and find the biggest perfect square that goes into your number, this will cut down on your total work!
Use “stars” to mark your perfect squares, this will make it easier when you have to find out what #s go in front of the “√” and behind it.

8. Websites

9. Fin