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Simplifying Radicals

Topic Radical Expressions Essential Question

How are radical expressions represented and how

can you

solve them?

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, ...

A List of Some Perfect Squares

64

225

1

81

256

4

100

289

9

121

16

324

144

25

400

169

36

196

49

625

Simplify

2

4

That was easy!

5

10

12

Perfect Square Factor Other Factor

Simplify

LEAVE IN RADICAL FORM

Perfect Square Factor Other Factor

Simplify

LEAVE IN RADICAL FORM

1. Simplify

Simplify

- .
- .
- .
- .

Combining Radicals

To combine radicals combine the coefficients of

like radicals

Hint In order to combine radicals they must be

like terms

Simplify each expression

Simplify each expression Simplify each radical

first and then combine.

Simplify each expression Simplify each radical

first and then combine.

Simplify each expression

Simplify each expression

Multiplying Radicals

To multiply radicals multiply the coefficients

and then multiply the radicands and then simplify

the remaining radicals.

Hint to multiply radicals they DO NOT need to be

like terms

Multiply and then simplify

(No Transcript)

Dividing Radicals

To divide radicals divide the coefficients,

divide the radicands if possible, and rationalize

the denominator so that no radical remains in the

denominator

That was easy!

Simplify

Uh oh There is a radical in the denominator!

Whew! It simplified!

Simplify

Uh oh Another radical in the denominator!

Whew! It simplified again! I hope they all are

like this!

This cannot be divided which leaves the radical

in the denominator. We do not leave radicals in

the denominator. So we need to rationalize by

multiplying the fraction by something so we can

eliminate the radical in the denominator.

42 cannot be simplified, so we are finished.

Simplify

Uh oh There is a fraction in the radical!

Since the fraction doesnt reduce, split the

radical up.

How do I get rid of the radical in the

denominator?

Multiply by the fancy one to make the

denominator a perfect square!

This can be divided which leaves the radical in

the denominator. We do not leave radicals in the

denominator. So we need to rationalize by

multiplying the fraction by something so we can

eliminate the radical in the denominator.

This cannot be divided which leaves the radical

in the denominator. We do not leave radicals in

the denominator. So we need to rationalize by

multiplying the fraction by something so we can

eliminate the radical in the denominator.

Reduce the fraction.

Simplify

X

Y3

P2X3Y

2X2Y

5C4D5

Simplify

Simplify

- .
- .
- .
- .

Challenge

Since there are no like terms, you can not

combine.

How do you know when a radical problem is done?

- No radicals can be simplified.Example
- There are no fractions in the radical.Example
- There are no radicals in the denominator.Example