Download Section 14-3: Simplifying Radical Expressions

Section 14-3: Simplifying Radical Expressions
Radical expression: any expression that includes a square root of a number or expression.
*A radical expression is simplified if the number under the square root is not a perfect
square or a multiple of a perfect square, and there can be NO radicals in the denominator
of a fraction.
Simplify each expression. Leave in radical form.
To get radicals out of the denominator of a fraction you must rationalize the
denominator. This process is what you do when you multiply both the numerator and the
denominator by the radical which makes the denominator a rational number (perfect
square). Make sure you reduce at the end.
???What happens when you have a radical in the denominator of a fraction, but it is a part
of a binomial? What can you multiply this by to get rid of the radical?
5
4 3
Notice what would happen if you just multiplied by
3.
Conjugates: a pair of binomials that are the same with the exception of the sign between
the two terms. When conjugates are multiplied (foiled) the radical is gone.
(2  5)(2  5) =
With this, the use of conjugates becomes critical when rationalizing denominators.
5
(4  3)

(4  3) (4  3)
Try a few of these:
5
a)
4 7
b)
4
3 2
c)
3
3 3
Radical Expression with Variables: Done the same as when you were dealing with
numbers. You just need pairs of variables to take them out of the square root sign.
1.
50x2
2.
27ab3
3.
49c6 d 4
4.
63x 2 y 5 z 2
5.
56m 2 n 4 p 3
6.
108r 2 s3t 6
Assignment: pg 618-619 # 16-41 all