## anonymous 5 years ago how would you simplify a cubed root radical of 25 times the radical of 125

1. anonymous

ok, you have 25^(1/3) * 125^(1/2)?

2. anonymous

yes

3. anonymous

ok, so how are 25 and 125 related?

4. anonymous

Both divisible by 5 and 25?

5. anonymous

ok, cool, so 25 = 5^2 and 125 = 5^2

6. anonymous

5^3, sorry

7. anonymous

oh okay yeah

8. anonymous

$\sqrt[3]{25} \times \sqrt{125} = 25^{1/3} \times 125^{1/2} = 5^{2/3} \times 5^{3/2} = 5^{4/6} \times 5^{9/6} = 5^{13/6}$ Feel free to correct me, this is my first time using this equation maker.

9. anonymous

omg it's too long for the page HAHA

10. anonymous

what is the equation maker?

11. anonymous

all right

12. anonymous

the answer is 5^{13/6} sorry it's too long haha

13. anonymous

yeah, that's how to do it easily hrwhyhry

14. anonymous

okay.. how on earth did you get that though?

15. anonymous

so you have 25=5^2, and 125=5^3....so you have (5^2)^(1/3) * (5^3)^(1/2)

16. anonymous

you can then add the exponents...here: $(5^2)^(1/3)$

17. anonymous

ohhhhh oka

18. anonymous

y mn

19. anonymous

(5^2)^(1/3) --> the square (2) and the (1/3) and now add together, 2/3

20. anonymous

okay thank you so much!

21. anonymous

so, you got it?

22. anonymous

i think soooo

23. anonymous

now how would you do x-$\sqrt[3]{3}\div \sqrt{12}$

24. anonymous

sorry its supposed to be the x- the 3 one

25. anonymous

????

26. anonymous

just a second

27. anonymous

thank you :)

28. anonymous

$(x-\sqrt[3]{3})/\sqrt{12}$

29. anonymous

is that the problem? is it equal to something?

30. anonymous

no thats the problem. You only have to simplify it

31. anonymous

ok

32. anonymous

so what is sqrt(12)?

33. anonymous

what are factors of 12?

34. anonymous

the square root of 4 times the square root of 3?

35. anonymous

right on, so sqrt(4) is simple, sqrt(3) is good because the problem has 3^(1/3)

36. anonymous

is the answer 1 over x^1/6 times 2?

37. anonymous

1/(x^1/6 * 2)?

38. anonymous

yes

39. anonymous

$(x-(3^{1/3}))/(2*(3^{1/2}))$

40. anonymous

i had that... i just dont kmow if u can get rid of the three

41. anonymous

so you can separate x and -3^(1/3) because they have the same denominator and they are part of a subtraction operation

42. anonymous

ok...

43. anonymous

thank u for the help by the way

44. anonymous

first look at 3^(1/3) / (2 * (3^1/2))

45. anonymous

np

46. anonymous

can you simplify that? focus on the 3's

47. anonymous

u can divide 3 by 3 and get one right

48. anonymous

when you divide by exponents you and subtract the exponents from values with the same base

49. anonymous

so 3^(1/3) / 3^(1/2) is 3^(1/3) * 3^-(1/2)...can you can add these exponents --> 1/3 = 2/6, 1/2 = 3/6, need to have similar fractions....so 2/6 - 3/6 = -1/6

50. anonymous

so you have 3^(-1/6)

51. anonymous

which is 1/(3^1/6)

52. anonymous

yes and u have to bring it below the division sign since it is negative?>

53. anonymous

yeah, like in the last message

54. anonymous

is the answer x over 3^1/6 *2

55. anonymous

wait, x-1

56. anonymous

(x-1)/(2*(3^1/6))

57. anonymous

$(x-1)/(2*(3^1/6))$

58. anonymous

$(x-1)/(2*(3^{1/6}))$

59. anonymous

how's that look?

60. anonymous

Thank you sooo much! I think thats right.....