anonymous
  • anonymous
√((18)/(36))=(√(2))/(2)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
\[\frac{ \sqrt{18} }{ \sqrt{36} }=\frac{ \sqrt{2} }{ 2 }\]
phi
  • phi
yes. you can see it is true by factoring each number into its prime factors 18 is 2*9 = 2*3*3 36 is 2*18= 2*2*9= 2*2*3*3 when these are under a square root \[ \frac{\sqrt{2\cdot 3\cdot 3}}{\sqrt{2\cdot 2\cdot 3 \cdot 3} }\] you can "pull out" pairs. in the top, 3*3 out of the square root becomes 3 in the bottom both 2 and 3 come out \[ \frac{3 \sqrt{2}}{2\cdot 3} \] we can divide top and bottom by 3 to simplify to \[ \frac{\sqrt{2}}{2} \]
phi
  • phi
of course, if you know 6*6=36 you can just replace the bottom sqrt(36) with 6 right away.

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anonymous
  • anonymous
so the question ask to simplify
phi
  • phi
sqrt(2)/2 is as simple as it gets. you could write it as 1/sqrt(2) but people do not sqrt's in the denominator.
anonymous
  • anonymous
ok. so i have another problem...it says to multiply and simplify \[(3\sqrt{10}-2\sqrt{2})^2=98-24\sqrt{5}\]
phi
  • phi
it looks like they gave you the answer. But to show how to do it, use FOIL on ( 3 sqrt(10) - 2 sqrt(2) )* ( 3 sqrt(10) - 2 sqrt(2) )
phi
  • phi
here is an example of how to do this http://www.khanacademy.org/math/algebra/polynomials/v/multiplying-binomials-with-radicals
anonymous
  • anonymous
so it will just be \[(3\sqrt{10}-2\sqrt{2})(3\sqrt{10}-2\sqrt{2})=98-24\sqrt{5}\]
phi
  • phi
yes, but I think they want you to do the multiplication and get the answer they show you.
anonymous
  • anonymous
how would you do that?
phi
  • phi
This video http://www.khanacademy.org/math/algebra/polynomials/v/multiplying-binomials and the other one posted go into the details.

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