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12.2 Square Roots
CORD Math
Mrs. Spitz
Spring 2007
Objectives
• Simplify rational square
roots, and
• find approximate values for
square roots
Assignment
• pp. 479-480 #5-51 all
How to read square roots
• 82 is read “eight squared
and means eight is used as
a factor two times.
• -8 is used as a factor two
times.
How to read square roots
• The opposite of squaring a
number is finding its square
root. To find the square
root of 64, you must find
two EQUAL factors whose
product is 64.
• Since 8 times 8 is 64, one
square root is 8. Since -8
times -8 is also 64, another
square root of 64 is -8.
Definition of a Square Root
• If x2 = y, then x is a square
root of y.
PARTS OF A RADICAL EXPRESSION
RADICAND
INDEX
3
RADICAL SIGN
64
What do these mean?
64  8
 64  8
indicate the principal square
root of 64.
indicates the negative square
root of 64.
 64  8
indicates both square roots of
64. Note this is read, “plus or
minus the square root of 64.”
Ex. 1: Find each square root.
81
Since 92 = 81, you know that
the square root is 9.
Ex. 2: Find each square root.
 0.09 
Since (0.3)2 = 0.09, you
know that the square root is
±0.3.
What if it doesn’t go evenly?
• Sometimes you may need
to use prime factorization
to find a square root of a
number.
Ex. 3: Find each square root.
 576 
576  2  2  2  2  2  2  3  3
 2 3
6
2
 (2  3)
3
 24
2
2
Since 242 = 576, you know
that the negative square root
is -24.
Ex. 4: Find each square root.
8
256
2
 4 2
2025 3  5
4
2 2
( 2 )
3 5
16 2
( )
45
16

45
Calculators
• If you happen to own one, and
you should. I would highly
recommend the TI-83 or 84 if
you are going to continue in
mathematics. If not, the TI30IIXS will suffice. It’s about $15 at
Wal-mart. In any case, you will
need one if you are doing
square roots or access to your
textbook on page 645 which
has a table of values.
Ex. 5. Find the square root of:
2209
Hit your 2nd button
Square root – 1st row 6 buttons
down.
Enter the number 2209 and click
enter or =
The value should be 47.
Ex. 6. Find the square root of:
 1236
Hit your 2nd button
Square root – 1st row 6 buttons
down.
Enter the number 1236 and click
enter or =
The value should be 35.1567917