It’s a Dog’s World!Multiplying and Dividing

Square Roots

Let’s talk about dogs….

Outside Dogs VS Inside Dogs

Meet “Coefficient”She’s an Outside Dog!!

Meet “Radicand”He’s an Inside Dog!!

Keep the Outside Dogs outside!

&

Keep the Inside Dogs inside!

Coefficient Radicand

*1.Multiply the Coefficients

2.Multiply the Radicands

3.Simplify

35*5 175 7*25 75

Multiply and then simplify

73*82 566 14*46

142*6 1412

204*52 1008 8010*8

2

5 5*5 25 5

2

7 7*7 49 7

2

8 8*8 64 8

2

x xx * 2x x

1.Divide the Coefficients

2. Divide the Radicands (if possible)

3.Rationalize the denominator (NO radicals in denominator)

4.Simplify

7

568 2*4

22

7

66 cannot be divided

by 7

but

NO radicals in the denominator

So we rationalize! How? Multiply the

fraction by something that will eliminate the

radical in the denominator.

7

7*7

6

49

42

7

42

42 cannot be simplified, so we are

finished.

Remember: NO radicals in the denominator !You MUST rationalize! How? Multiply the fraction by something that will eliminate the radical in the denominator.How about 1??

10

5

2

2*2

1

2

2

Remember: NO radicals in the denominator !You MUST rationalize! How? Multiply the fraction by something that will eliminate the radical in the denominator.How about 1??Then Simplify!!!

12

3

3

3*

12

3

36

33

6

33

2

3Reduce

the fraction.

3X

XX

=

=

XX *2

YY 45Y

=

= YY 2

2X

6Y

264 YXP

244 YX

10825 DC

= X

= Y3

= P2X3Y

= 2X2Y

= 5C4D5

Have you learned how to multiply and divide

expressions containing square roots?

Keep the Outside Dogs outside!

&

Keep the Inside Dogs inside!

Coefficient Radicand

Don’t even think about

mixing coefficients

and radicands!!!