Simplification of radical expressions is easy! Generally, you want to find two numbers, one being a perfect square (4, 9, 16, 25 etc) and the other being any number, that multiply to give you the root your’re looking to simplify!
In your example, you’re looking to simplify ##2sqrt(45)##.
First, find two numbers (one being a perfect square) that multiply to give you ##sqrt(45)##.
Options are:
1 and 45 3 and 15 5 and 9
Here, it looks like 9 and 5 are going to work, since one of them is a perfect square!
Knowing this we can say, by the properties of radicals:
## 2*sqrt(9)*sqrt(5) ##
Notice the ##sqrt(9)##? You can simplify that to 3!
##2*3*sqrt(5)##
Multiply the 2 and 3 together and you get:
##6sqrt(5)##
That’s it! Just follow the same steps as I have for any radical problems and you’ll be good with any problem that comes your way! Hopefully I helped you out! 🙂
