√
Simplifying
Radicals
<<Only perfect squares can be
taken out of radicals>>
√1
1
√4
2
√9
3
√16
4
√25
5
√36
6
√49
7
√64
8 they
When
radicals include variables,
are still
√81simplified the same9way
1)√100
Factor the radicand into
10its
factors and expand the
√121
11
variable(s).
√144
12
2) Bring any variable listed twice in
the radicand to the outside.
*
X =
Steps to simplify:
1. Divide the number under the
radical by the largest perfect
square that can go into it.
2. Simplify the perfect square,
and keep the multiplier
Examples:
under the radical.
 √75
The biggest perfect square that can be
divided into 75 is 25
 √75= √25x5
Examples:
√x4 = √x*x*x*x
X
If there is not a perfect
square under a radical,
you can SIMPLIFY it!
X2
√Y3Z6 = √y*y*y*x*x*x*x*x*x
√25 becomes 5, the √5 remains under
the radical
Final Answer:
5√3