My Algebra I students are having lots of problems with simplifying radical expressions. It seems that they have run across a concept that eludes them. I am posting about this topic to provide several more examples.
First, we find the prime factorization of 18. If you need help with this concept, go here.
√18 = √(2•3•3)
Since the 3 is repeated twice, we can pull it out from under the square root symbol. Therefore,
√18 = 3√2
Now my students would be asking what happens if you have variables?
√24x3y2 = √(2•2•2•3•x•x•x•y•y)
Pull out everything that is repeated twice - 2, x, y. Leave everything else under the radical symbol.
Some other places to visit for more details on this concept are here and here and here.
If you are one of my students and would like some extra credit, please visit those sites and comment here on whether or not they were helpful.