Adding and Subtracting Radical Expressions - Problem 4

This is a challenging problem because I have X's and Y's that need to be simplified in my radicands. Well let’s check it out. This first product cannot be simplified any further. This guy also cannot be simplified any further. Let’s look at this one. I have 2 times the square root of y² x.

Well the square rot of y² you guys probably know is y; let me show you what I mean. 2 times the square root of y² times the square root of x. The square root of y² is just y, so what this third piece is just 2y square root of x.

Once I have it written like this I can see that these three pieces are going to combine pretty easily. 3 square roots of x plus y square roots of x plus 2y square root of x. Okay well let’s look at the things that are outside the square roots. I have 3 plus y plus 2 more y 3 plus y plus 2y is 3 plus 3y, that’s what’s going to be outside and then my radical is square root of x. Be really careful to use parenthesis on this 3 plus 3y piece because this whole thing is being multiplied by the square root of x. That’s some thing that a lot of students will make a mistake on.

The most common wrong error for this problem would look like this. This means only the 3y is multiplied by root x. I don’t want that, I want this whole 3 plus 3y piece to get multiplied my x

So there it is, that’s my final answer and I found it by simplifying noticing I had the same radicands and then combining the numbers that the outside the square roots to get that guy.