Simplify radicals

ObjectivesThe student will be able to:

1. simplify square roots, and2. simplify radical expressions.

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, -114. Find the square root:

215. Find the square root:

3. Find the square root: 121

441

2581

59

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. SimplifyFind a perfect square that goes into 605.

605

121 5121 5

11 5

Simplify

1. .

2. .

3. .

4. .

2 18

72

3 86 236 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

604 15

4 152 15

7. Simplify 2 14 3 21Multiply the coefficients and radicals.

6 2946 49 6

6 649

42 66 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

14

15

8. Simplify.

Divide the radicals.

108

3

1083

366

Uh oh…There is a

radical in the denominator!

Whew! It simplified!

9. Simplify

8 2

2 8

4 14

422

Uh oh…Another

radical in the denominator!

Whew! It simplified again! I hope they all are like this!

10. Simplify

57

57

757 7

3549

357

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!