What is the square root of 12 multiplied by the square root of 6?

1 Answer
Sep 17, 2015

Answer:

#sqrt(12)sqrt(6) = 6sqrt2#

Explanation:

To evaluate #sqrt12sqrt6# we must first remember that we can join these two roots together

#sqrtasqrtb = sqrt(ab)# as long as they're not both negative, so
#sqrt12sqrt6 = sqrt(12*6)#

While we can just multiply these two, we know that #12 = 2*6#, so we know that #12*6 = 2*6*6 = 2*6^2#

Therefore #sqrt(12*6) = sqrt(2*6^2)#.
Now, since there's no additions or differences being done we can take it out of the root, but to get out it loses its square. So

#sqrt(12)sqrt(6) = 6sqrt2#

And now there's no more manipulation to be done.