Download Rules of Simplification

135
10.1-10.3 Graphing Review
Important Vocabulary to know!
A Quadratic Function written in standard form looks like:
Name 3 other words that mean the same thing as the Solution to an equation…
_______________________, ________________________, ________________________
The graph of a Quadratic Function is called a _____________________.
The formula for the vertex is:
If the vertex is on the top of the parabola it is called a __________________.
If the vertex is on the bottom of the parabola it is called a ____________________.
A quadratic function can have ___________, __________ or __________ solutions.
Graph the Following Quadratics and Find the Zeros of the Function.
1. x  2 x  3  0
2.  x  6 x  9
2
2
y
y
10
10
x
-10
10
x
-10
10
-10
-10
Solution(s): _______________________
Zero(s): __________________________
10. 2 x 2  2 x  3
y
10
Vertex:
x
y
x
-10
Root(s): ______________________
10
-10
Simplifying Square and Cubic Roots
136
When we raise a number to the second power we ‘square’ that number. Squaring a
number means to multiply the number by itself. The square of an integer is called a
perfect square.
List the first 10 perfect squares.
Find the square roots.
12
________
62
________
1 =  ________
36 =  _______
22
________
72
________
4 =  ________
49 =  _______
32
________
82
________
9 =  ________
64 =  ________
42
________
92
________
16 =  ________
81 =  ________
52
________
102
________
25 =  ________
100 =  _______
If x  49 , then x = ____ or ____
If x 2  25 , then x = ____ or ____
2
Only use  if you are solving for x!
The symbol
is called a radical sign and always represents a non-negative square root.
The number under the radical sign is called the radicand (or argument). Together the
radical sign and the radicand is called a radical and an algebraic expression containing a
radical is called a radical expression.
How do you find the square root of a number that is not a perfect square? You
can either estimate or simplify them.
Estimate 14
9
14
16
3
?
4
Based on this information, you know 14 is between 3 and 4. Use the square
root key on the calculator to find a closer approximation.
Estimate the following values (Between which two whole numbers).
a. 27
b. 21
c. 45
Note:
You cannot have a negative number under the square root sign. For example:
9 is
not a real number since you cannot square any number and get a
negative number.
Rules of Simplification
Simplifying square root expressions without using decimals




Factor the radicand using a factor tree
Circle “pairs” of numbers
Remove a “representative” of each “pair”
Multiply to simplify
1. 50  25  2  25  2  5 2
or
50  5  5  2  5 2
Circle Pairs since you are
simplifying a square root
2. 108 x3  2  2  3  3  3  x  x  x  2  3  x 3  x  6 x 3x
3.
60
60
3
3



 3
20
1
1
20
Cube Roots
The cube root of 8 is written 3 8  2 , since 23  8 (which means 2  2  2 = 8).
The cube root of -8 is written 3 8  2 because -2  -2  -2 = -8.
Notice that you can have a negative under the
cube root sign…the answer is then negative.
A Few Perfect Cubes…
Find the Cube Root:
13 = ______
43 = ______
3
1 = ______
3
64 = ______
23 = ______
53 = ______
3
8 = ______
3
125 = ______
33 = ______
63 = ______
3
27 = ______
3
216 = ______
Something to think about:
1)
3
64
2) 3 64
3)  3 64
Simplifying cube root expressions without using decimals




1.
3
Factor the radicand using a factor tree
Circle “three of a kinds” of numbers
Remove a “representative” of each “set of three”
Multiply to simplify
32  3 2  2  2  2  2  2 3 2  2  2 3 4
Circle ‘Three of a Kinds’ since
you are simplifying a cube roots
2.
3
432 x 4 y 2  3 2  2  2  2  3  3  3  x  x  x  x  y  y  2  3  x 3 2  x  y  y  6 x 3 2 xy 2
Final Answer!
Examples: Simplify each Square or Cube Root.
1.
12
4. 3 160
7. - 3 144
2.
27 x 2
3
3. - 48x 3 y 2
5.
16 x
49 x
6. 5 3 108
8.
450xy 3
9.
75
25
HW: Simplify each square or cube root. (No Decimals in your answer!)
1.
100
2.  100
3.
100
4.
64
6.  3 64
48x3
8.
9.  192x 2 y 3
10.
5.
7.
3
3
3
64
128x4
98
137
11. 242
13.
19
49
15. 3 20x5
17. 3 128
19.
242xy 3
12. 7 21
14. - 3 135x 4 y 3
16.
128
64
18.
5
45
20.
3
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