Algebra/Trig Review - Pauls Online Math Notes - Lamar University

Algebra/Trig ReviewSo, what do we do if we know that we want the negative number? Simple. We add aminus sign in front of the square root as follows− 4 =− ( 2)=− 2This gives the negative number that we wanted and doesn’t violate the rule thatsquare root always return the positive number!Okay, let’s finally do this problem. For the most part it works the same as theprevious one did, we just have to be careful with the absolute value bars.4 8 15 4 4 4 4 4 4 316xy= 16xx yyy y= 2x x y y y4y3= 22 34 3x y y2 34 3= 2x y yNote that I could drop the absolute value on the2x term because the power of 2 will2give a positive answer for x regardless of the sign of x. They do need to stay on they term however because of the power.RationalizingRationalize each of the following.1.3xyx +ySolutionThis is the typical rationalization problem that you will see in an algebra class. Inthese kinds of problems you want to eliminate the square roots from the denominator.To do this we will use2 2( a+ b)( a− b) = a − b .So, to rationalize the denominator (in this case, as opposed to the next problem) wewill multiply the numerator and denominator by x − y. Remember, that torationalize we simply multiply numerator and denominator by the term containing theroots with the sign between them changed. So, in this case, we had x + y and sowe needed to change the “+” to a “-”.Now, back to the problem. Here’s the multiplication.3xy( x − y)3xy x − y=x + y x − y x−y( )( )( )© 2006 Paul Dawkins 11http://tutorial.math.lamar.edu/terms.aspx