## haterofmath 2 years ago √((18)/(36))=(√(2))/(2)

1. haterofmath

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

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

3. phi

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

4. haterofmath

so the question ask to simplify

5. 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.

6. haterofmath

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

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

9. haterofmath

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

10. phi

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

11. haterofmath

how would you do that?

12. phi

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