objectives the student will be able to: 1. simplify square roots, and 2. simplify radical...
TRANSCRIPT
ObjectivesThe student will be able to:
1. simplify square roots, and
2. simplify radical expressions.
SOL: A.3
Designed by Skip Tyler, Varina High School
In the expression , is the radical sign and
64 is the radicand.
If x2 = y then x is a square root of y.
1. Find the square root:
8
2. Find the square root:
-0.2
64
64
0.04
11, -11
4. Find the square root:
21
5. Find the square root:
3. Find the square root: 121
441
25
815
9
6.82, -6.82
6. Use a calculator to find each square root. Round the decimal answer to the nearest hundredth.
46.5
1 • 1 = 12 • 2 = 43 • 3 = 9
4 • 4 = 165 • 5 = 256 • 6 = 36
49, 64, 81, 100, 121, 144, ...
What numbers are perfect squares?
1. Simplify
Find a perfect square that goes into 147. 147
147 349
147 349
147 7 3
2. Simplify
Find a perfect square that goes into 605.
605
121 5
121 5
11 5
Simplify
1. .
2. .
3. .
4. .
2 18
72
3 8
6 236 2
Look at these examples and try to find the pattern…
How do you simplify variables in the radical?
x7
1x x2x x3x x x4 2x x5 2x x x6 3x x
What is the answer to ? x7
7 3x x x
As a general rule, divide the exponent by two. The remainder stays in the
radical.
Find a perfect square that goes into 49.
4. Simplify 49x2
249 x7x
5. Simplify 258x254 2x
122 2x x
Simplify 369x
1. 3x6
2. 3x18
3. 9x6
4. 9x18
Multiply the radicals.
6. Simplify 6 10
60
4 154 152 15
7. Simplify 2 14 3 21Multiply the coefficients and radicals.
6 294
6 49 66 649
42 6
6 67
Simplify
1. .
2. .
3. .
4. .
24 3x44 3x
2 48x448x
36 8x x
How do you know when a radical problem is done?
1. No radicals can be simplified.Example:
2. There are no fractions in the radical.Example:
3. There are no radicals in the denominator.Example:
8
1
4
1
5
8. Simplify.
Divide the radicals.
108
3
108
3
366
Uh oh…There is a
radical in the denominator!
Whew! It simplified!
9. Simplify
8 2
2 8
4 1
4
4
2
2
Uh oh…Another
radical in the denominator!
Whew! It simplified again! I hope they all are like this!
10. Simplify
5
7
5
7
75
7 7
35
49 35
7
Since the fraction doesn’t reduce, split the radical up.
Uh oh…There is a fraction in the radical!
How do I get rid of the radical in
the denominator?
Multiply by the “fancy one” to make the denominator a
perfect square!