Date:________________
Aim #45: How do we simplify radicals?
Do Now:
1) Evaluate 32
2) Evaluate
Simplifying Radicals
√
index
radicand
radical
The radicand is the number under the radical sign.
The index represents the root you are taking.
The index is assumed to be 2 (taking the square root) if
nothing is written
A radical is in simplest form when:
-The factors of the radicand are 1 and non perfect square
Example
Since the factors of 5 are 1 and
5 (a non perfect square) it is in simplest
radical form
-Radicand does not contain a fraction.
-Radicals do not appear in the denominator of a fraction.
perfect squares:
To simplify: find the largest perfect square which will divide
evenly into the number under your radical sign.
Example:
How do we simplify radicals with an index other than 2 ?
Perfect cubes:
Example:
1) Simplify
Simplify each radical
1) 2) 3)
How do we simplify radicals with variables?
1)
2)
3)
4)
Sum It Up!
When simplifying radicals we first look for ________ perfect
square or cube factors and exponents that are divisible by the
_______. Then the remaining factors are left under the radical.