Download Algebra_1B_files/Lecture 9A

Ch 9: Quadratic Equations
A) Simplifying Radicals
Objective:
To simplify radical expressions.
Definitions
Square Root
A square root is a number that when multiplied by itself
equals a given number.
Radicand
The radicand is the number (or expression) inside the radical
sign. The radical sign looks similar to a check mark (√).
Perfect Square
A perfect square is a number (or expression) in which every
term has a pair leaving nothing inside the radical.
These can be found on the diagonal of any multiplication table
Prime Number
A number that can only be divided by 1 and itself.
Examples: 2, 3, 5, 7, 11, 13, 17, 19……….
Multiplication Table
Perfect Squares
x
1
1 1
2
3
4
5
6
7
8
9
10
2
3
4
5
6
7
8
9
10
4
9
16
25
36
49
64
81
100
Rules
1) Factor the radicand into its prime numbers.
2) Look for pairs inside the radicand.
3) The number that has a pair goes OUTSIDE of the
radical and the non-paired numbers stay inside
the radical.
Negative radicands:
The square root of a negative number does not exist!
You cannot multiply a number by itself and end
up with a negative number.
Example 1
Example 2
Example 3
√12
√48
√25
2
2
6
6
3
2
3 2
4
2
√(223)
2√3
5 5
8
√(22223)
22√3 = 4√3
√(55)
2
5
Perfect Square!
Example 4
Example 5
√-18
-2√8
3
2
2
6 -1
√-9
3 3 -1
4
3
2
√(233-1)
−2√(222)
3√-2
not a
Real Number
Example 6
2
2−2√2 = −4√2
√(33-1)
3√-1
not a
Real Number
Classwork
1) √27
2) √32
3√3
4√2
3) √24
4) √-8
2√6
2√−2
not a
Real Number
Classwork
5) √8x2
2x√2
7) √16xy2
4y√x
6) √12x
2√3x
8) √-25x2y2
5xy√−1
not a
Real Number