anonymous one year ago Will fan & medal Simplify: 2 (^3sqrt108)

1. anonymous

@dan815 @zepdrix @Directrix

2. Directrix

Is this supposed to be: 2 ^ (3sqrt108) ? Two raised to the (3 times square root of 108) power?

3. anonymous

No, its just the number 2 being multiplied by the sqrt of 108 that has ^3 in front of the sqrt sign... I learned in my lesson that it means 108^1/3

4. anonymous

@Directrix

5. johnweldon1993

Oh okay $$\large 2(\sqrt[3]{108})$$

6. anonymous

Yes!!

7. johnweldon1993

So try and think about cubed roots $$\large 2^3 = 8$$ <---can this be evenly divided into 108? $$\large 3^3 = 27$$ <---what about this? $$\large 4^3 = 64$$ <--- or this? We know 64 cannot be evenly divided into 108..so ignore that...but in what way ...can we manipulate the numbers 3 and 2 to break down 108? *Remembering the key is cubed root*

8. anonymous

Hmmm... I'm thrown off by the 3 and 2 you gave me to work with.. Not really sure what I'm supposed to do :/

9. johnweldon1993

Well the reason why I'm giving you that is because if you think about it $\large \sqrt[3]{x^3} = x$ right? the 3 and the 3 cancel leaving just 'x'...so if we can find something that is raised to the third power....this can be simplified greatly So hint* (kinda a big one lol) $$\large 3^3 * 4$$ what does that equal?

10. anonymous

27 times 4 is 108 ;p

11. anonymous

Wait!!

12. anonymous

You may be reading too much into this because the goal is not to cancel out that exponent.. It still remains in the answer

13. johnweldon1993

Exactly :P So if we take your original question $\large 2(\sqrt[3]{108})$ and write it as $$\large 2\sqrt[3]{(3^3 * 4)}$$ that is the same ***and the exponent will still be in the answer btw :P *** just a way of breaking it down

14. anonymous

My answer choices are: 16 3^sqrt18 8 3^sqrt6 5 3^sqrt4 6 3^sqrt4

15. anonymous

Ohh okay haha got it

16. johnweldon1993

mmhmm i see the one i'm aiming at ;P

17. anonymous

Lol!!!

18. johnweldon1993

Okay SO remember how i said $\large \sqrt[3]{x^3} = x$ Well...lookey what we have here... $\large 2(\sqrt[\color \red{3}]{\color \red{3^3} * 4})$

19. anonymous

oh!!! i know the answer now ;p

20. johnweldon1993

So now if we re-write this as $\large 2(3\sqrt[3]{4})$ I believe you can do the rest ;P

21. anonymous

so its 6 3^sqrt4

22. johnweldon1993

BAM! lol "ju got et chicha" ;p

23. anonymous

Bahaha thanks bby ;*

24. johnweldon1993

Anytime puddin ;* lol