Simplifying radicals
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Simplifying Radicals. 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. = 5. This is a piece of cake!. = 10. = 12. Perfect Square Factor * Other Factor. Simplify. = . = . = . = .

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Perfect squares l.jpg
Perfect Squares

64

225

1

81

256

4

100

289

9

121

16

324

144

25

400

169

36

196

49

625


Slide3 l.jpg

Simplify

= 2

= 4

= 5

This is a piece of cake!

= 10

= 12


Slide4 l.jpg

Perfect Square Factor * Other Factor

Simplify

=

=

=

=

LEAVE IN RADICAL FORM

=

=

=

=

=

=


Slide5 l.jpg

Perfect Square Factor * Other Factor

Simplify

=

=

=

=

LEAVE IN RADICAL FORM

=

=

=

=

=

=


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Combining Radicals

+

To combine radicals: combine the coefficients of like radicals





Slide10 l.jpg

Perfect Square Factor * Other Factor then combine.

Simplify

=

=

=

=

LEAVE IN RADICAL FORM

=

=

=

=

=

=




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Multiplying Radicals then combine.

*

To multiply radicals: multiply the coefficients and then multiply the radicands and then simplify the remaining radicals.



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Dividing Radicals then combine.

To divide radicals: divide the coefficients, divide the radicands if possible, and rationalize the denominator so that no radical remains in the denominator


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That was easy! then combine.


Slide18 l.jpg

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.


Slide19 l.jpg

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.


Slide20 l.jpg

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.


Slide21 l.jpg

Simplify 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.

= X

= Y3

= P2X3Y

= 2X2Y

= 5C4D10


Slide22 l.jpg

Simplify 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.

=

=

=

=


Slide23 l.jpg

= 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.

=

?

=

=


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