Hi! Could someone explain how to solve this? $$\sqrt[3]{4}\times \sqrt[2]{8}$$ thank you!

Question

Hi! Could someone explain how to solve this? $$\sqrt[3]{4}\times \sqrt[2]{8}$$ thank you! <3

shadowfiend · Answer

Hm. Is that right or is it the opposite? ($\sqrt[3]{8} \times \sqrt[2]{4}$ ) ?

anonymous · Answer

sorry, for some reason, the equation writer won't work. and nope, it's not. :D the answer according to my answer key is 4 sqrt[6]{2), but i don't know how to get it.

anonymous · Answer

If the problem is typed correctly, use index notation and put in powers of 2:

cubrt4 = 4^(1/3) = ((2^2)^(1/3) = 2^(2/3)

sqrt8 = ((2^3)^(1/2)) = 2^(3/2)

Multiply the two by adding indices to get 2^(7/6) which is not the same as your answer, unfortunately

anonymous · Answer

i'm really sure that the answer is $$4\sqrt[6]{2}$$ i even checked it with my calculator myself. but i just don't know how to get it. :(

anonymous · Answer

$$\sqrt[3]{4}\sqrt{8} $$Square the expression$$\left(\sqrt[3]{4}\sqrt{8}\right)^2=16\ 2^{1/3} $$Take the square root of the result.$$\sqrt{16\ 2^{1/3}}=4\ 2^{1/6}=4 \sqrt[6]{2} $$

shadowfiend · Answer

Hero in da heezy. Nice one robtobey.

anonymous · Answer

Aw shucks.  Thanks.