Download Square Roots - Cloudfront.net

11.1 and 11.2 Radicals
List all the perfect squares:
Square Roots
• Symbol:
x
or
x
1
2
• Every positive number has both positive
and negative square roots.
• Principal: just the positive answer
Radical
Sign
25  5 and -5
25  5
“Principal” Square Root is the positive 5.
Simplify:
81
9
Because (9)2 = 81
 64 ±8
36
(6)2  -36
(-6)2  -36
Not possible
Rational Numbers
• Whole #, fraction, decimal that ends or
repeats, square root that is a perfect square
7
7
yes ,
1
1.3
13
yes ,
10
0.3333
1
yes,
3
Irrational Numbers
• Square roots that are not perfect squares
• Decimal never ends and does not repeat.
• Examples of irrational numbers:

2
Identify the number as irrational or rational
6

1
35
36
Identify the rational number:
A.
48
B.
49
C.
50
D.
51
49  7
Real Numbers: All the rational
and all the Irrational numbers.
-25 is NOT a real number. 52  25
 5
Real Numbers
0
Rational
2
Numbers
9
5
7
Irrational

Numbers
2
 25
Radical Expressions
(an expression written under a radical)
18
x
x 9
2
Radicand
(the expression written
under the radical)
The radicand must be positive!
If there is a variable in the
radicand:
radicand  0
and solve for the variable to
find the values of x that make
the expression a real number.
Determine the values of x that make
the expression a real number.
2x 1
2x  1  0
2x  1
1
x
2
Determine the values of x that make
the expression a real number.
x 3
2
x 3 0
2
x  3
2
ManySolutions
Perfect Square Radicands
Rule:
If the radicand contains a variable
the square root needs to be in
absolute values
x  |x|
2
Explanation
x x
5 5
( x)   x
(5)  5
2
2
2
2
Simplify:
x  1
2
| x 1|
Simplify:
x  8x  16
2
x  4
2
|x4|
Simplify:
25x
2
| 5x |
or 5 | x |
Simplify:
1
x
2
1 2
x
4
1
x
2
Homework
worksheet