Simplify the Following Radicals

March 8

 A square root function is a function containing a square root with the independent variable in the radicand.  The easiest way to graph a function is to create an x and y table. Graph y = xy

 Now when you are graphing square roots there is no need for you to include negative x values in your table.  Remember taking the square root of a negative number creates no real roots, so you will be unable to graph non-real roots.  So to find what number to start with we need to find the x-value that will give you a real number answer

For example what if we had We would set x – 2 = 0 and solve for x. Radicand

xy

xy

xy

xy

 Recall that we would break down the radicand into their prime factors, and then circle, cross, ‘n’ toss. Radical or Square Root  Radicand

Example: 1. 2.

It is important to remember back to our exponents unit, and think about how we expanded expressions. For example: 54n 7

 For radical exponents where the exponent of a variable inside the radical is even and the resulting simplified exponent is odd, you must use absolute value to ensure nonnegative results

3. 4.

1. 2.

3.4.

1. 2.

 A fraction containing radicals is in simplest form if no radicals are left in the denominator. The Quotient Property of Square Roots and rationalizing the denominator can be used to simplify radical expressions that involve division. Examples: 1.2.

 Worksheet on the back of the notes!