## DF001 one year ago Help with algebra: 3/^3rad2

1. DF001

$\frac{ 3 }{ \sqrt[3]{2} }$

2. DF001

For one of the rule, the denominator can not be radical but, how can I get rid of that?

3. DF001

I have to simplify this problem

4. DF001

may i ask if the denominator is (2)^1/9

5. anonymous

ups my bad, its 2/3

6. DF001

i can see it now, it's the ^n(radA^m) property

7. anonymous

|dw:1442814606283:dw|

8. DF001

in converting (2)^2/3, what is used is one of the exponential properties, am I correct?

9. anonymous

|dw:1442814720626:dw|

10. anonymous

yes

11. DF001

|dw:1442814768602:dw|

12. DF001

I got a different answer on Mathway and it is 3^3rad2/2

13. DF001

|dw:1442814815877:dw|

14. anonymous

so going back.|dw:1442814759487:dw|

15. anonymous

Ignore the other pictures from before, made a mistake on these.

16. DF001

How can I get |dw:1442814937004:dw|

17. DF001

I get the part up to the latest picture u sent me but, the answer I got from mathway is weird

18. anonymous

|dw:1442814933276:dw|

19. anonymous

you do the same process again with the cube root of 4

20. DF001

Im confused with the process now. i usually multiple the denominator to the numerator but, this question is the very first that i've ever done :/

21. anonymous

|dw:1442815066254:dw|

22. DF001

no matter how i multiple the denominator by itself, it's still a radical :(

23. anonymous

you teacher wants you to get rid of the root being on the denominator. The way to cancel it is by multiplying it by itself again such as this.|dw:1442815238734:dw|

24. DF001

yes, I did it that way but, the denominator came out to be ^3rad

25. anonymous

Well we now have the cube root of 4, we have to do the same process once again until be can simplify it off and not have a root on the denominator.

26. anonymous

|dw:1442815330274:dw|

27. anonymous

|dw:1442815374173:dw|

28. anonymous

|dw:1442815438983:dw|

29. DF001

How can I simplify it by 2

30. DF001

I can see that rad8 would be 2rad2 if there isn't a 3 as the index

31. anonymous

ow just noticed I went on a circle.. my bad lol

32. anonymous

|dw:1442815657071:dw|

33. anonymous

Forgot to do that on the denominator otherwise you go back to the 3/(2)^(1/3)

34. DF001

I think I get it alot better now

35. DF001

I can see that rad4 is simplified to 2x2

36. anonymous

|dw:1442815852580:dw|

37. DF001

could I ask why the denominator turned to 2 when its 2x2x2

38. DF001

|dw:1442815914490:dw|

39. DF001

im only confused on that part

40. DF001

i was wondering what happened to the index 3

41. anonymous

|dw:1442815923532:dw|

42. anonymous

|dw:1442816056423:dw|

43. anonymous

when you square root something, for example 4 then it is equals to 2 because 2*2 = 4 right?

44. DF001

oh I see now, 2^3=8 thus, the denom is 2

45. anonymous

In this case is cube too meaning you need the same number 3 times and multiply it to get the answer. In this case 8 would be 2*2*2 = 8

46. DF001

I understand now, thank you very much :)

47. anonymous

Cube root*

48. anonymous

Sure, no problem :)