ObjectivesThe student will be able to:

1. simplify square roots, and

2.simplify radical expressions.

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

11, -11

4. Find the square root:

21

5. Find the square root:

3. Find the square root:

5

9

It is a number that has a whole number square root.

What is a Perfect Square?

149

162536

49, 64, 81, 100, 121, 144, ...

What numbers are perfect squares?

1. Simplify

Find a perfect square that goes into 147.

147 7 3

What are some strategies for finding the perfect squares in radicands?

The square root is simplified when there are no perfect squares left in

the radicand.

2. Simplify

Find a perfect square that goes into 605.

11 5

Compare and Contrast

Find the square root of with your calculator.

Now simplify the square root of

This means 31 and 0.18

This means 18 times

Are these answers equivalent?

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?

1x x2x x3x x x4 2x x5 2x x x6 3x x

What is the answer to ?

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

7x

5. Simplify 258x

122 2x x

Simplify

1. 3x6

2. 3x18

3. 9x6

4. 9x18

Multiply the radicals.

6. Simplify

60

2 15

7. Simplify Multiply the coefficients and radicals.

6 294

42 6

Simplify

1. .

2. .

3. .

4. .

24 3x44 3x

2 48x448x

How do you know when a radical problem is done?

1. No perfect squares are in the radicand. 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

366

Uh oh…There is a

radical in the denominator!

Whew! It simplified!

Simplify.

Divide the radicals. Uh oh…There is a

radical in the denominator!

Whew! It simplified!

Simplify.

Divide the radicals.

Simplify

4 1

4

4

2

2

Uh oh…Another

radical in the denominator!

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

Simplify

Simplify

5

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 same square root to make the

denominator a perfect square!

Simplify

Multiply by the same square root to make the

denominator a perfect square!

in two different ways.

Simplify

Describe which way you prefer and explain why.

Closure:

Explain how you can tell if a radical expression is in

simplified form.