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It’s a Dog’s World!Multiplying and Dividing
Square Roots
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Let’s talk about dogs….
Outside Dogs VS Inside Dogs
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Meet “Coefficient”She’s an Outside Dog!!
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Meet “Radicand”He’s an Inside Dog!!
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Keep the Outside Dogs outside!
&
Keep the Inside Dogs inside!
Coefficient Radicand
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*1.Multiply the Coefficients
2.Multiply the Radicands
3.Simplify
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35*5 175 7*25 75
Multiply and then simplify
73*82 566 14*46
142*6 1412
204*52 1008 8010*8
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2
5 5*5 25 5
2
7 7*7 49 7
2
8 8*8 64 8
2
x xx * 2x x
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1.Divide the Coefficients
2. Divide the Radicands (if possible)
3.Rationalize the denominator (NO radicals in denominator)
4.Simplify
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7
568 2*4
22
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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.
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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
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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.
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3X
XX
=
=
XX *2
YY 45Y
=
= YY 2
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2X
6Y
264 YXP
244 YX
10825 DC
= X
= Y3
= P2X3Y
= 2X2Y
= 5C4D5
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Have you learned how to multiply and divide
expressions containing square roots?
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Keep the Outside Dogs outside!
&
Keep the Inside Dogs inside!
Coefficient Radicand
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Don’t even think about
mixing coefficients
and radicands!!!