Download Radical Review

Radical Review
Multiplying Radicals
Multiply “outside” number x “outside” number.
Multiply “inside” number x “inside” number.
Examples: Multiply. If you get any perfect squares, do the square root.
a. 12  3 =
b. 2 3 4 2 =
 
c.


3 7 5 
White Board Activity:
Practice: Multiply and simplify.
a. 4  6
c.

5 2 7
 
b. 3 5 4 3 =

Simplifying Radicals
A radical is in simplest form if no perfect square factors other than 1 are in the “inside” number”.
Perfect squares: 1, 4, 9, 16, 25, 36, etc.
Steps:
1. Prime factor the number “inside” the radical.
2. Look for pairs. Write each pair as a perfect square number.
3. Rewrite the “inside” as a product of the perfect squares and the “left overs”.
4. Take square roots of the perfect square numbers placing these answers “outside” the
radical. Leave the “left overs” inside the radical.
5. Multiply the “outside” numbers together.
Multiply the “inside” numbers together.
Example: Simplify the expression.
a. 48
b. 5 96
White Board Activity:
Practice: Simplify the expression.
a. 80
b. 7 27
c.
72
d. 4 24
Dividing Radicals
Divide the “outside” number by the “outside” number if possible.
Divide the “inside” number by the “inside” number if possible.
Reduce the “outside” part of a fraction if possible.
Reduce the “inside” part of a fraction if possible.
Take a square root when possible.
Example: Simplify.
12 15
a.
3 3
c.
2 3
6 12
36
16
White Board Activity:
Practice: Simplify.
25 30
a.
6 6
c.
b.
b.
5 2
15 18
25
81
A simplified radical does not have a radical term in the denominator.
To clear radicals from a denominator, you must rationalize the denominator.
This means multiply both the numerator and denominator of the fraction by the radical term from the
denominator.
Example: Rationalize and simplify.
1
a.
3
c.
2
3 5
.
7
12
White Board Activity:
Practice: Rationalize and simplify.
2
a.
5
c.
b.
5
18
b.
5
2 7
.