This week in Pre Calc 11 we looked at different things. In this weeks blog post I am going to explain how to do mixed radicals.
When doing mixed radicals I prefer to make a factor tree. It helps me be able to visualize it and easily see what my perfect square, cube and so on is going to be without having to do very much work. I find that when putting bigger numbers into a mixed radical a factor tree helps me keep my questions organized so when I look back at it later I am easily able to identify what I did.
Step 1: When you get your question the first step is to break it down into its prime factors. As you can see I broke down 108 all the way down to it’s prime factors via a factor tree.
Step 2: The second thing I do is take my prime factors and put them in a cubed root. I then circle my groups of three numbers, what I mean by that is because there is three three’s I know that is going to be a perfect cube.
Step 3: In this final step I pulled out the three. The three came from the three 3’s multiplied together but because they’re in a cubed root they’re going to equal 3 anyways. And as you can see there is a 4 inside the cubed root. Well that 4 comes from the two left over numbers, which in this case happens to be 2 and 2 so when multiplied together gives us 4.
Tip* Don’t forget if it’s a cubed root and fourth root and so on to make sure you put the little three or whatever it is on the square root.
It’s that simple! Just three simple steps. I will do one more example.
In this example you can see I followed the same steps, the only difference was that at my second step I needed to see 4 of the same numbers because it was a fourth root.
And that is all you need to know for mixed radicals. The last thing I am going to add is if at your second step, if you needed a cubed root and you didn’t have three of the same numbers that mixed radical wouldn’t work and your answer would be “not possible”. Just remember these three simple steps and you will be good!