## haterofmath Group Title √((18)/(36))=(√(2))/(2) one year ago one year ago

1. haterofmath Group Title

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

2. phi Group Title

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 $\frac{\sqrt{2}}{2}$

3. phi Group Title

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

4. haterofmath Group Title

so the question ask to simplify

5. phi Group Title

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.

6. haterofmath Group Title

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

7. phi Group Title

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) )

8. phi Group Title

9. haterofmath Group Title

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

10. phi Group Title

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

11. haterofmath Group Title

how would you do that?

12. phi Group Title

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