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9.3 Simplifying Radicals

Square Roots

- Opposite of squaring a number is taking the

square root of a number. - A number b is a square root of a number a if b2

a. - In order to find a square root of a, you need a

that, when squared, equals a.

If x2 y then x is a square root of y.

In the expression , is the radical

sign and64 is the radicand.

- 1. Find the square root
- 8 or -8

3. Find the square root

- 11, -11
- 4. Find the square root
- 21 or -21
- 5. Find the square root

6. Use a calculator to find each square root.

Round the decimal answer to the nearest

hundredth.

- 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, ...

Simplify

2

4

5

This is a piece of cake!

10

12

Product Rule for Radicals

Simplifying Radicals

Example

- Simplify the following radical expressions.

No perfect square factor, so the radical is

already simplified.

Perfect Square Factor Other Factor

Simplify

LEAVE IN RADICAL FORM

Perfect Square Factor Other Factor

Simplify

LEAVE IN RADICAL FORM

Perfect Square Factor Other Factor

Simplify

LEAVE IN RADICAL FORM

1. Simplify

- Find a perfect square that goes into 147.

2. Simplify

- Find a perfect square that goes into 605.

Simplify

- .
- .
- .
- .

Multiplying Radicals

To multiply radicals multiply the coefficients

and then multiply the radicands and then simplify

the remaining radicals.

6. Simplify

- Multiply the radicals.

7. Simplify

- Multiply the coefficients and radicals.

Multiply and then simplify

(No Transcript)

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

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!

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.

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.

8. Simplify.

- Divide the radicals.

Uh oh There is a radical in the denominator!

Whew! It simplified!

9. Simplify

Uh oh Another radical in the denominator!

Whew! It simplified again! I hope they all are

like this!

10. 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!