Saiyan one year ago 4. What is the simplest form of the expression. sqrt 3-sqrt 6/sqrt 3 + sqrt 6

1. Saiyan

I would like some help because somewhere in the equation i am making a mistake in multiplying it by the conjugate.

2. Nnesha

3. Nnesha

so we can find ur mistake :=)

4. Nnesha

what is the conjugate ?

5. Saiyan

|dw:1438037552571:dw|

6. Nnesha

right now multiply $\huge\rm \frac{ (\sqrt{3} - \sqrt{6})(\sqrt{3} - \sqrt{6}) }{ (\sqrt{3}+ \sqrt{6}) (\sqrt{3}-\sqrt{6}) }$ now apply foil method at the top and bottom

7. anonymous

8. Saiyan

$\sqrt{3}^2-\sqrt{6}^2/(\sqrt{3}-\sqrt{6})^2$

9. Nnesha

well parentheses at the numerator are the same but not at the denominator careful abt signs

10. Nnesha

$\huge\rm \frac{ (\sqrt{3} \color{reD}{-} \sqrt{6})(\sqrt{3} \color{REd}{-} \sqrt{6}) }{ (\sqrt{3}\color{Red}{+} \sqrt{6}) (\sqrt{3}\color{Red}{-}\sqrt{6}) }$ familiar wit the foil method ?

11. Saiyan

yes

12. Nnesha

good so apply that :=)

13. Saiyan

14. Nnesha

is it 3^2 under the square root ?

15. Saiyan

no

16. Nnesha

$(\sqrt{3})^2$ like this ?

17. Saiyan

yes

18. Nnesha

well no that's right

19. Nnesha

|dw:1438038779860:dw| try again $\huge\rm \color{ReD}{\sqrt{3}}({\sqrt{3}} -\sqrt{6}) \color{ReD}{- \sqrt{6}}(\sqrt{3}- \sqrt{6})$ distribute

20. Saiyan

ok hold on

21. Saiyan

$\sqrt{9}-\sqrt{18}-\sqrt{18}+\sqrt{36}$

22. Nnesha

perfect take square rot of 9 and 36 combine - s quare root of 18

23. Saiyan

3+6-sqrt36

24. Nnesha

what is square root of 36 ?

25. Nnesha

$\sqrt{9}\color{Red}{-\sqrt{18}-\sqrt{18}}+\sqrt{36}$ combine those two terms

26. Saiyan

3-sqrt36+6

27. Nnesha

$\sqrt{9}\color{Red}{-\sqrt{18}-\sqrt{18}}+\sqrt{36}$ $3 ~~\color{REd}{??????} +6$ square root of 36 is 6 and now -sqr{18} - sqt{18} isn't equal to sqrt{36

28. Nnesha

it is same as x^2 + x^2 = 2x^2

29. Saiyan

-18-18=36

30. Saiyan

-36

31. Nnesha

nope it's not just -18 let's say $\sqrt{18}=x^2$ so -x^2 -x^2 =what ?

32. Saiyan

-2x^2

33. Nnesha

yes right now change x^2 with sqrt{18) so u get ?

34. Saiyan

18

35. Nnesha

we assume that sqrt{18} is x^2 so just replace x^2 by sqrt{18} you will get $-2\sqrt{18}$

36. Nnesha

you need to combine them not multiply

37. Nnesha

38. Nnesha

just like x+x = 2x same way $-\sqrt{18}-\sqrt{18} = -2\sqrt{18}$

39. Saiyan

oh ok

40. Nnesha

yes so numerator is $\frac{ \color{Red}{3}-2\sqrt{18}+\color{Red}{6} }{ }$ combine like terms

41. Nnesha

and then apply foil method at the denominator $(\sqrt{3}+\sqrt{6})(\sqrt{3}-\sqrt{6}) = ?$

42. Saiyan

so it 9-2 to the sqrt 18

43. Nnesha

yep right and then you have to factor sqrt 18

44. Saiyan

ok i got the answer thx

45. Nnesha

u sure ?

46. Saiyan

yep now i understand

47. Saiyan

thx

48. Nnesha

alright then . let me know if u need help my pleasure :=)