BioHazard9064
  • BioHazard9064
Algebra Help
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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BioHazard9064
  • BioHazard9064
Is the simplified form of \[2\sqrt{3}* 2\sqrt{6}\] rational?
anonymous
  • anonymous
Do you have an idea on what to do and are just unsure?
BioHazard9064
  • BioHazard9064
Answers: A. Yes B. No

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BioHazard9064
  • BioHazard9064
No I don't really know
anonymous
  • anonymous
Ok, you can think about multiplying the numbers in front of the radical signs and the numbers under the radical signs separately.
BioHazard9064
  • BioHazard9064
ok so 2*2 is 4
anonymous
  • anonymous
Yes, and what is 3 * 6?
BioHazard9064
  • BioHazard9064
18
anonymous
  • anonymous
Ok so we have\[(2 \sqrt3 )(2\sqrt6) = 4\sqrt{18}\]
BioHazard9064
  • BioHazard9064
so is that rational ?
anonymous
  • anonymous
There is a 3^2 underneath the radical so you can pull that out\[4\sqrt{18} = 12\sqrt{2}\]
anonymous
  • anonymous
12 may be rational, but the sqrt 2 is not, so their product isn't rational either.
BioHazard9064
  • BioHazard9064
So its B
anonymous
  • anonymous
Yes, it isn't rational
BioHazard9064
  • BioHazard9064
so lets say though its like this \[2\sqrt{3}-2\sqrt{3}\] is that rational?
BioHazard9064
  • BioHazard9064
I think not?
anonymous
  • anonymous
Well is zero rational? What does it mean to be rational anyways? To be rational means that a number can be represented as some fraction with either the numerator or denominator being odd.
BioHazard9064
  • BioHazard9064
and you cant really have 0 in a fraction
anonymous
  • anonymous
Well we can right? I can put \[2\sqrt3 - 2\sqrt3 = 0 = \dfrac{0}{1}\]
BioHazard9064
  • BioHazard9064
oh ok I see that now so it would be rational
anonymous
  • anonymous
Yes
BioHazard9064
  • BioHazard9064
ok thanks allot
anonymous
  • anonymous
No problem, good luck in your studies.
BioHazard9064
  • BioHazard9064
thanks I need it xD

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