Transcript 12.5 Simplifying Square Roots CORD Math Mrs. Spitz Spring 2007 Objectives • Simplify square roots, and • simplify radical expressions that contain variables.

12.5 Simplifying Square Roots
CORD Math
Mrs. Spitz
Spring 2007
Objectives
• Simplify square roots, and
• simplify radical expressions that contain
variables.
Assignment
• pp. 495-496 #5-53
If x2 = y then x is a square root of y.
In the expression 64
is the radical sign and
64 is the radicand.
1. Find the square root: 64
8
2. Find the square root:  0.04
-0.2
3. Find the square root:  121
11, -11
4. Find the square root: 441
21
25
5. Find the square root: 
81
-5/9
6. Use a calculator to find each
square root. Round the decimal
answer to the nearest hundredth.
 46.5
6.82, -6.82
What numbers are perfect squares?
1•1=1
2•2=4
3•3=9
4 • 4 = 16
5 • 5 = 25
6 • 6 = 36
49, 64, 81, 100, 121, 144, ...
1. Simplify.
147
Find a perfect square that goes into 147.
147  49 g 3
147  7 3
2. Simplify
605
Find a perfect square that goes into 605.
605  121 g 5
605  11 5
3. Simplify.
x
7
For variables, divide the exponent by
two. 7 ÷ 2 = 3 with remainder 1
x x
7
3
x
The remainder stays in the radical.
4. Simplify.
49x
2
Find a perfect square that goes into 49.
49x  7x
2
5. Simplify. 6  10
Multiply the radicals.
6 g 10  60
Simplify:
60
60  4 g15
60  2 15
6. Simplify. 2 14  3 21
Multiply the coefficients and the radicals.
6 294
6 49 g 6
6 g7 6
42 6
7. Simplify.
Divide the radicals.
108
3
36
6
108
3
8
2
8. Simplify.
2 8
8 2
8 2
1
1

4
4
4
2 8 2 4
4
4
2
2
9. Simplify.
5
7
On the board!
Answer:
35
7