Download Simplifying Radicals

Solving
Equations
A quadratic equation is an equation equivalent to one of the
form
2
ax  bx  c  0
Where a, b, and c are real numbers and a  0
So if we have an equation in x and the highest power is 2, it is quadratic.
To solve a quadratic equation we get it in the form above
and see if it will factor.
x  5x  6
2
-5x + 6
-5x + 6
Get form above by subtracting 5x and
adding 6 to both sides to get 0 on right side.
x 2  5x  6  0
x  3x  2  0
x  3  0 or x  2  0
Factor.
Use the Zero property of
multiplication and set each
factor = 0 and solve.
x 3
x2
ax  bx  0
c0
2
What if in standard form, c = 0?
2 x  3x  0
2
x2 x  3  0
We could factor by pulling an x
out of each term.
Factor out the common x
Use the Null Factor law and set each
factor = 0 and solve.
x  0 or 2x  3  0
3
x  0 or x 
2
If you put either of these values in for x
in the original equation you can see it
makes a true statement.
Remember standard form for a quadratic equation is:
ax  bx
0x  c  0
2
ax  c  0
2
In this form we could have the case where b = 0.
When this is the case, we get the x2 alone and then square root both sides.
2x  6  0
2
+6
+6
2x  6
2
2
2
x 3
Get x2 alone by adding 6 to both sides and then
dividing both sides by 2
Now take the square root of both
sides remembering that you must
consider
considerboth
boththe
thepositive
positive and
and
negative
negative root.
root.
x  3
2
Let's
check:
 
2
2 3 6  0
66  0


2
2  3 6  0
66  0
Another example:
3 x  18  0
2
In this form we could have the case where b = 0.
When this is the case, we get the x2 alone and then square root both sides.
3 x  18  0
2
+ 18
+ 18
3x  18
2
3
3
x 6
Get x2 alone by adding 18 to both sides and then
dividing both sides by 3
Now take the square root of both
sides remembering that you must
consider
considerboth
boththe
thepositive
positive and
and
negative
negative root.
root.
x 6
2
Let's
3
check:
 6
2
 18  0
18 18  0

3  6

2
 18  0
18 18  0
To simplify radicals: look for a
square factor or a pair of factors
Square Root of a product
36 
94
36  6  3  2 
ab =
a
9
b
You can break a square root into
two square roots over a
multiplication sign.
4
A pair square number under the
Radical
12 
2
43 
4
3
The square of the square
number can be calculated to
simplify the radicand
3
You should know your square
numbers
1•1=1
2•2=4
3•3=9
4 • 4 = 16
5 • 5 = 25
6 • 6 = 36
49, 64, 81, 100, 121, 144, 169, 196, 225, 256
A pair of numbers under the Radical
22
= 22
The square and square root
undo each other
=2
pair _ of _ numbers _ multiplied
= original number
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
You have to make sure that your
final answer is simplified all the way
80
4  20
=
= 2 20
= 2
45
= 22 5
= 4
5
LEAVE IN RADICAL FORM
Your turn
Simplify
72
84
147
605
LEAVE IN RADICAL FORM
Homework
Worksheet