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