Question #64872

1 Answer
Larry Leitch-Casey
Nov 29, 2015

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!

Explanation:

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! :)

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