Transcript Simplifying Radicals

Radical: the square root
Radicand: number under
square root
To simplify radicals: look for a
square factor or a pair of factors
Square Root of a product
a b =
a
b
You can break a square root into
two square roots over a
multiplication sign.
When you find a square number
under the Radical you take the
square root of it.
12 
2
3
43 
4
3
A pair of numbers under the Radical
2 2
=
2
2
 2
The square and square root
undo each other and the number
“pops” out
LEAVE IN RADICAL FORM
You have to make sure that your
final answer is simplified all the way
48
=
4  12
= 2 12
= 2
43
= 22 3
=4 3
LEAVE IN RADICAL FORM
If you don’t know how to start, try to
find any number that is a factor and
see what happens
405 =
5  81
= 9
5
LEAVE IN RADICAL FORM
Your turn
40
27
72
∙
To multiply radicals: simplify each
radicand then multiply.
Look for a pair of numbers or a
square number
Simplify then Multiply
5  35  5  5  7  5 7
2 8 3 7  2 4 2 3 7  2 23 2 7
 12 14
2 5  4 20  2 5  4 4 5
 8  5  2  80
Your Turn
21  7
5  30  3
6 18  5 14
Homework
• Pg. 526 # 4 to 40 even