Simplifying a square root. For this particular problem what we’re looking at is the square root of 32x to the 4th. We’re trying to simplify this given that x is going to be a positive number.
So in order to do this, there’s a couple of ways of doing it. You can hopefully over time you’ll get good at it and just be able to do it in one or two steps but just to sort of walk you through the process of how we can get to that point what we can do is break this up.
This square root can go to both the 32 and the x to the 4th, so we could rewrite it as square root of 32 times the square root of x to the 4th. And we’re saying then is the square root of 32. What perfect square goes into 32? 16 and that leaves us with the square root of 16 times 2. Square root of 16, is 4 so we can take out a 4, leaving us with 4 root 2. That’s just dealing with the constant term of 32.
Now we need to say okay, what times what gives us x to the 4th? X times x gives us x², x² times x² gives us x to the 4th, so this is just going to be x². Throwing everything together what we end up with is 4x² and let’s try to spread that out a little bit so it doesn’t look a little so funny, 4x² times the square root of 2.
Okay, so just using our laws of being able to simply square roots, whenever you have a perfect square you’re able to take it out and whatever isn’t a perfect square is left underneath the square root.