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Bell Ringer• Use the Pythagorean Theorem to
find the length of the hypotenuse.
10.1 Simplifying Square Roots
Objectives: The student will be able to:
1. simplify square roots
In the expression , is the radical sign and
64 is the radicand.
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?
Simplify
1. .
2. .
3. .
4. .
2 18
72
3 8
6 236 2
Multiply the radicals.
3. Simplify 6 10
60
4 154 152 15
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
Simplify.
Divide the radicals.
108
3
108
3
366
Uh oh…There is a
radical in the denominator!
Whew! It simplified!
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!
Homework
• Page 539-540
#12-20 even, 26-30 even, 36-42 even