9.3 Simplifying Radicals - PowerPoint PPT Presentation

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9.3 Simplifying Radicals

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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. – PowerPoint PPT presentation

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Title: 9.3 Simplifying Radicals


1
9.3 Simplifying Radicals
2
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.

3
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

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

5
6. Use a calculator to find each square root.
Round the decimal answer to the nearest
hundredth.
  • 6.82, -6.82

6
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, ...

7
Simplify
2
4
5
This is a piece of cake!
10
12
8
Product Rule for Radicals
9
Simplifying Radicals
Example
  • Simplify the following radical expressions.

No perfect square factor, so the radical is
already simplified.
10
Perfect Square Factor Other Factor
Simplify




LEAVE IN RADICAL FORM






11
Perfect Square Factor Other Factor
Simplify




LEAVE IN RADICAL FORM






12
Perfect Square Factor Other Factor
Simplify




LEAVE IN RADICAL FORM






13
1. Simplify
  • Find a perfect square that goes into 147.

14
2. Simplify
  • Find a perfect square that goes into 605.

15
Simplify
  1. .
  2. .
  3. .
  4. .

16
Multiplying Radicals

To multiply radicals multiply the coefficients
and then multiply the radicands and then simplify
the remaining radicals.
17
6. Simplify
  • Multiply the radicals.

18
7. Simplify
  • Multiply the coefficients and radicals.

19
Multiply and then simplify
20
(No Transcript)
21
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

22
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
23
That was easy!
24
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.
25
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.
26
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.
27
8. Simplify.
  • Divide the radicals.

Uh oh There is a radical in the denominator!
Whew! It simplified!
28
9. Simplify
Uh oh Another radical in the denominator!
Whew! It simplified again! I hope they all are
like this!
29
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!
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