Transcript 12.2 Square Roots CORD Math Mrs. Spitz Spring 2007 Objectives • Simplify rational square roots, and • find approximate values for square roots.

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

64   8
indicate the principal square
root of 64.
indicates the negative square
root of 64.
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.
256

2025
(
(
2
3 5
45

16
45
3 5
4
4
2
16
2
)
2
)
8
2
2
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