Transcript Perfect Square

Simplified Radical Form
Objective:
1) Describe simplified Radical Form
2) Simplify radical expressions by
a) Factoring out perfect squares
b) Combine Like Terms
Vocabulary
Square Root: If a2 = b, then a is the square root
of b.
Ex:
625  25
m2  m
Most numbers have 2 square roots.
Principal (positive)
Negative
 36  6
121  11
To indicate both:
 9  3
Vocabulary
Perfect Square: Numbers whose square roots are
integers.
Ex:
169  13
Approximate vs. Exact Values for Irrational Numbers
Square Roots of Negative Numbers
Simplified Radical Form
In order for a radical expression to be simplified, the
following must be true.
1) The expression under the radical sign has no
perfect square factors other than 1.
2) For sums and differences, like radical terms are
combined
3) There are no fractions under the radical.
4) There are no radicals in the denominator of a
fraction.
Multiplication Property of Square
Roots
For any numbers a ≥ 0 and b ≥ 0,
a b  a  b
Ex:
5  6  30
6  2 3
Using the Multiplication Property to
Simplify Radical Expressions
“Factor” Perfect Square factors out from under the
radical.
Simplify
Simplified Radical Form
(Continued)
Objective:
Simplify radical expressions by
a) Eliminating Fractions from under the
radical
b) Rationalize the denominator
Division Property of Square
Roots
For any numbers a ≥ 0 and b > 0,
a

b
Ex:
3

4
3
3

2
4
a
b
Simplify
4
49
48
3x 2
242
27 x
2
x
3
Rationalizing the Denominator*
*Means to get rid of an irrational number in the denominator of a fraction
To Rationalize the Denominator of a fraction, multiple the numerator
and denominator by a radical that will create a perfect square
under the radical of the denominator.
3
2

2
2

3 2
2 2

3 2
3 2

2
4
Simplify
2
6
15
18
72
10