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Radicals. Objective: To review working with radical expressions. 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.

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Radicals

Radicals

Objective: To review working with radical expressions.


Perfect squares
Perfect Squares

64

225

1

81

256

4

100

289

9

121

16

324

144

25

400

169

36

196

49

625


Radicals

Simplify

= 2

= 4

= 5

This is a piece of cake!

= 10

= 12


Radicals

Perfect Square Factor * Other Factor

Simplify

=

=

=

=

LEAVE IN RADICAL FORM

=

=

=

=

=

=


Radicals

Perfect Square Factor * Other Factor

Simplify

=

=

=

=

LEAVE IN RADICAL FORM

=

=

=

=

=

=


Warm up
Warm up

  • Simplify:

  • 1.

  • 2.

  • 3.


Multiplying dividing radicals

Multiplying & Dividing Radicals

Objective: To simplifying products and quotients of radicals.


Radicals

Multiplying Radicals

*

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



Radicals

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


Radicals

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.


Radicals

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.


Radicals

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.


Radicals

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


Radicals

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.

=

=

=

=


Radicals

= 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.

=

=

=


Warm up1
Warm up 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.

  • Simplify

  • 1.

  • 2.

  • 3.


Adding subtracting radicals

Adding & Subtracting Radicals 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.

Objective: To simplify sums & differences of radicals.


Radicals

Combining Radicals 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.

+

To combine radicals: combine the coefficients of like radicals


Simplify each expression
Simplify each expression 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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