1. jackoo

$3 \sqrt[3]{24}$

2. klimenkov

Hint:$\sqrt[3]{24}=\sqrt[3]{8\cdot3}=\sqrt[3]8\cdot\sqrt[3]{3}$

3. jackoo

Thank you!

4. klimenkov

5. jackoo

$6\sqrt[3]{3}$

6. klimenkov

Very nice.

7. jackoo

Could you help me with another question?

8. jackoo

$3\sqrt{x+4}-2=13$

9. klimenkov

What is the problem?

10. klimenkov

What cant you do?

11. klimenkov

Solve for $$\sqrt{x+4}$$.

12. klimenkov

Hey! Are you here?

13. jackoo

Yes, I am sorry

14. jackoo

couldn't I just do 4-2 giving me 2 so then I do x+2=13?

15. jackoo

x+2=13 -2 -2 x=11

16. jackoo

idk

17. klimenkov

Can you solve $$3y-2=13$$ ?

18. jackoo

y=5

19. klimenkov

Yes. Think if $$y=\sqrt{x+4}$$.

20. klimenkov

If you make a substitution $$y=\sqrt{x+4}$$, you will get $$\sqrt{x+4}=5$$. Do you know what $$\sqrt{\phantom{a}}$$ sign means?

21. jackoo

square root

22. klimenkov

What does square root means?

23. jackoo

a number multiplied by itself?

24. klimenkov

Can you tell me what does $$\sqrt{16}$$ mean?

25. jackoo

4?

26. klimenkov

Yes. But Also -4 too. -4*(-4)=16. So what can you say about $$\sqrt{x+4}=5$$ ?

27. jackoo

x=1?

28. jackoo

I don't think I know

29. klimenkov

See the analogy. Try to think. Compute $$\sqrt{36}, \sqrt{25}, \sqrt{\frac14}$$.

30. jackoo

alright. 6,5,2

31. klimenkov

Check the last one.

32. klimenkov

$$\sqrt x$$ is the inverse function for $$x^2$$. $$\sqrt x$$ is a number that squared must be $$x$$. $$(\sqrt x )^2=x$$. Think about last one.

33. jackoo

I still think it's1

34. klimenkov

Compute $$\sqrt{\frac14}$$.

35. jackoo

2

36. klimenkov

$$2^2\neq\frac14$$

37. klimenkov

Try again.

38. jackoo

1/4

39. klimenkov

$$\left(\frac14\right)^2\neq\frac14$$. Try again.

40. jackoo

So I have to square it?

41. klimenkov

You have to find $$\sqrt{\frac14}$$ using the definition I wrote above.

42. jackoo

.5

43. jackoo

.5*.5=1/4

44. klimenkov

Yes. Thats it. Now back to $$\sqrt{x+4}=5$$. Can you solve it?

45. jackoo

Would I plug something in x?

46. klimenkov

Ok. Can you solve this: $$\sqrt x = 2$$ ?

47. jackoo

4

48. klimenkov

Yes. Thats it. Now back to $$\sqrt{x+4}=5$$. Can you solve it?

49. jackoo

25?

50. klimenkov

$$\sqrt{25+4}\neq5$$

51. jackoo

21

52. klimenkov

Bingo. You solved this by your own. Congratulations!

53. jackoo

It has to be that's why thought of 25 =5

54. jackoo

Thank you:)!!

55. klimenkov

You are welcome.