Download Square Roots and Cube Roots

Square Roots and Cube Roots
4.6
Perfect Squares
•1
•4
•9
• 16
• 25
• 36
• 49
• 64
• 81
• 100
• 121
• 144
• 169
• 196
• 225
Square Root
• A square root of a number is one of its two
equal factors.
• Notation: radical sign is used to indicate a
nonnegative square root.
Positive and Negative Signs
36  6
 36  1 36  6
 36  6
36  no  real  solution
Find each square root
1.) 64
8
2.)  121
 11
3.)  256
 16
4.) 9
no  real  solution
Estimate to the Nearest Integer
• For numbers that are not perfect squares, find
the two perfect square the number is
between.
• Graph the square root on the number line to
determine which perfect square it is closest
to.
Estimate the nearest Integer
1.) 60
49  60  64
7  60  8
8
2.)  18
 16   18   25
4   18  5
4
Cube Roots
• A cube root of a number is one of its three
equal factors
3
• If x  y then 3 y
Perfect Cube Roots
•1
•8
•27
•64
•125
•216
•343
•512
•729
•1000
Every Integer has exactly one cube
root
• The cube root of a positive number is positive
• The cube root of zero is zero
• The cube root of a negative number is
negative
Find the Cube Root
3
1.) 125
5
2.) 3 729
9
Estimate to the nearest integer
2.) 39
1.) 3 72
3
64  3 72  3 125
3
3
27  3 39  3 64
4  72  5
3  39  4
4
3
3
3
Homework
Page 172 (16-38) even