Will fan & medal
Simplify: 2 (^3sqrt108)

Question

Will fan & medal
Simplify: 2 (^3sqrt108)

anonymous · Answer

@dan815 @zepdrix @Directrix

directrix · Answer

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

anonymous · Answer

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

anonymous · Answer

@Directrix

johnweldon1993 · Answer

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

anonymous · Answer

Yes!!

johnweldon1993 · Answer

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*

anonymous · Answer

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 :/

johnweldon1993 · Answer

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?

anonymous · Answer

27 times 4 is 108 ;p

anonymous · Answer

Wait!!

anonymous · Answer

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

johnweldon1993 · Answer

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

anonymous · Answer

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

anonymous · Answer

Ohh okay haha got it

johnweldon1993 · Answer

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

anonymous · Answer

Lol!!!

johnweldon1993 · Answer

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

anonymous · Answer

oh!!! i know the answer now ;p

johnweldon1993 · Answer

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

anonymous · Answer

so its 6 3^sqrt4

johnweldon1993 · Answer

BAM! lol "ju got et chicha" ;p

anonymous · Answer

Bahaha thanks bby ;*

johnweldon1993 · Answer

Anytime puddin ;* lol