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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
Perfect Squares

64

225

1

81

256

4

100

289

9

121

16

324

144

25

400

169

36

196

49

625

slide3

Simplify

= 2

= 4

= 5

This is a piece of cake!

= 10

= 12

slide4

Perfect Square Factor * Other Factor

Simplify

=

=

=

=

LEAVE IN RADICAL FORM

=

=

=

=

=

=

slide5

Perfect Square Factor * Other Factor

Simplify

=

=

=

=

LEAVE IN RADICAL FORM

=

=

=

=

=

=

slide6

Combining Radicals

+

To combine radicals: combine the coefficients of like radicals

slide10

Perfect Square Factor * Other Factor

Simplify

=

=

=

=

LEAVE IN RADICAL FORM

=

=

=

=

=

=

slide13

Multiplying Radicals

*

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

slide16

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

slide18

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

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

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

Simplify

= X

= Y3

= P2X3Y

= 2X2Y

= 5C4D10

slide23

=

=

?

=

=