Objectives

The student will be able to:

1. simplify square roots, and 2. simplify radical expressions.

SOL: A.13

Designed by Skip Tyler, Varina High School

If x 2 = y then x is a

square root

In the expression , is the

radical sign

64 and 64 is the

radicand

.

of y.

1. Find the square root:

8

2. Find the square root: 

-0.2

64 0.04

3. Find the square root: 

11, -11

4. Find the square root:

21

5. Find the square root:  441 25 81  5 9 121

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, ...

Find a perfect square that goes into 147.

147  147  49 49 147  7 3 3 3

2. Simplify 605 Find a perfect square that goes into 605.

121 5 121 5 11 5

1.

2.

3.

4.

.

.

2 18 .

.

3 8 6 2 36 2 Simplify 72

How do you simplify variables in the radical?

x

7 Look at these examples and try to find the pattern…

x x

2

x x

4

x x

1 3 5 6  

x x

 

x x x

2  

x x

2 3

x x

7 

x

3

x x

7 As a general rule, divide the exponent by two. The remainder stays in the radical.

4. Simplify 49

x

2 Find a perfect square that goes into 49.

49 7

x x

2 5. Simplify 4 2

x

25 2

x

12 2

x

8

x

25

1. 3x 6 2. 3x 18 3. 9x 6 4. 9x 18 Simplify 9

x

36

6. Simplify 6  10 Multiply the radicals.

60 4 15 4 15 2 15

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

6 6 294 49 6 6 49 6 7 6 6 42 6

Simplify 6

x

3 8

x

1.

2.

3.

4.

4 .

x

2 3 .

4 3

x

4 .

x

2 48 .

48

x

4

How do you know when a radical problem is done?

1. No radicals can be simplified.

Example: 8 2. There are no fractions in the radical.

Example: 1 3. There are no radicals in the denominator.

Example: 1 4 5

Whew! It simplified!

8. Simplify.

108 3 Divide the radicals.

108 3 Uh oh… There is a radical in the denominator!

36 6

9. Simplify 8 2 2 8 4 1 4 Whew! It simplified again! I hope they all are like this!

4 2 2 Uh oh… Another radical in the denominator!

10. Simplify 5 7 Uh oh… There is a fraction in the radical!

Since the fraction doesn’t reduce, split the radical up.

5 7  5 7 7 7  35 49  35 7 How do I get rid of the radical in the denominator?

Multiply by the “fancy one” to make the denominator a perfect square!