√((18)/(36))=(√(2))/(2)

Question

anonymous · Answer

$$\frac{ \sqrt{18} }{ \sqrt{36} }=\frac{ \sqrt{2} }{ 2 }$$

phi · Answer

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 · Answer

of course, if you know 6*6=36  you can just replace the bottom sqrt(36) with 6 right away.

anonymous · Answer

so the question ask to simplify

phi · Answer

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 · Answer

ok. so i have another problem...it says to multiply and simplify
$$(3\sqrt{10}-2\sqrt{2})^2=98-24\sqrt{5}$$

phi · Answer

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 · Answer

here is an example of how to do this http://www.khanacademy.org/math/algebra/polynomials/v/multiplying-binomials-with-radicals

anonymous · Answer

so it will just be $$(3\sqrt{10}-2\sqrt{2})(3\sqrt{10}-2\sqrt{2})=98-24\sqrt{5}$$

phi · Answer

yes, but I think they want you to do the multiplication and get the answer they show you.

anonymous · Answer

how would you do that?

phi · Answer

This video http://www.khanacademy.org/math/algebra/polynomials/v/multiplying-binomials and the other one posted go into the details.