AngelaB97 one year ago what is 6 --- ^3√4

1. AngelaB97

what is |dw:1441484588912:dw|

2. AngelaB97

how do you rationalize it?

3. triciaal

|dw:1441486622928:dw|

4. triciaal

to rationalize the denominator means to get rid of the radical. multiply by 1 expressed as a fraction

5. AngelaB97

before you continue can i just ask is there some sort of rule for what you did when you crossed out those fractions. Meaning, could i be able to do that with any sort of radical that i want to rationalize?

6. triciaal

|dw:1441486781234:dw|

7. triciaal

rules for exponents the nth root is the same as a fractional exponent.

8. AngelaB97

the answer is supposed to be |dw:1441486876177:dw|

9. Excalibur0126

Or in decimal form, 3.7797631...

10. triciaal

|dw:1441486898347:dw|

11. triciaal

give me a minute

12. AngelaB97

sure

13. triciaal

|dw:1441487116337:dw||dw:1441487355866:dw|

14. triciaal

I think I messed up on something @zepdrix please correct

15. zepdrix

Hey Angela :) In order to rationalize this thing, you'd like the power on the 4 to be a 1. I like the first step that Tricia applied, writing the 4 with a rational exponent.$\large\rm \frac{6}{\sqrt[3]{4}}=\frac{6}{4^{1/3}}$So we don't want a 1/3 power, we want a 1 power down there. What do we have to add to 1/3 to get 1?

16. AngelaB97

hey :)) we have to add 2/3

17. zepdrix

Good good good. We would like 2/3 exponent, we'll leave the base the same. So we actually want to multiply top and bottom by $$\large\rm 4^{2/3}$$ Our rules of exponents will give us $$\large\rm 4^{1/3}\cdot4^{2/3}=4^{1/3+2/3}$$ in the denominator!

18. triciaal

@zepdrix thanks

19. zepdrix

$\large\rm \frac{6}{4^{1/3}}\left(\frac{4^{2/3}}{4^{2/3}}\right)=\frac{6\cdot4^{2/3}}{4^{3/3}}$Ok with that step Angela? :o

20. triciaal

|dw:1441488139781:dw|

21. AngelaB97

6 * 42/3 divided by 4

22. zepdrix

$\large\rm \frac{\color{orangered}{6}\cdot 4^{2/3}}{\color{orangered}{4}}$Mmmm k good. This can be simplified a little bit further since 6 and 4 share a common factor.

23. AngelaB97

so on the bottom we get 2 and the 6 turns into a 3?

24. zepdrix

$\large\rm \frac{3\cdot4^{2/3}}{2}$Yayyyy good job \c:/

25. AngelaB97

so we don't need to do any further simplifying? because the answer in my book shows |dw:1441488618998:dw| @zepdrix

26. zepdrix

OH interesting :O Ok sec I think about it

27. zepdrix

Ok maybe this is a better route to take then..$\large\rm \frac{6}{4^{1/3}}=\frac{3\cdot2}{4^{1/3}}=\frac{3\cdot2}{(2^2)^{1/3}}=\frac{3\cdot2}{2^{2/3}}$

28. zepdrix

I'm rewriting the 6 as 3*2. I'm rewriting 4 as 2 squared. and then applying exponent rule, when we have a power and a power like that, we multiply. So 2 times 1/3 gave me 2/3 for the power on the 2.

29. zepdrix

$\large\rm =\frac{3\cdot2^1}{2^{2/3}}$And now we can apply one of our exponent rules from here: $$\large\rm \frac{x^{a}}{x^b}=x^{a-b}$$ Do you see how we can apply that to the 2's?

30. AngelaB97

yes thank you very much

31. triciaal

@AngelaB97 sorry if we confuse you but hopefully you understand more about the rules of exponents and how to rationalize it is very easy to make mistakes if not careful

32. AngelaB97

@zepdrix @triciaal thank you both for your help!

33. zepdrix

yay team \c:/

34. triciaal

welcome anytime