Question

Which choice is equivalent to the quotient below? square root of 12 over 2 square root of 2

Answer 1

do you mean
\[ \frac{\sqrt{12}}{2 \sqrt{2}}\]
?

if so I would write 12 as 3*2*2
and \[ \sqrt{12}= \sqrt{3\cdot 2 \cdot 2} \]
if you have a "pair" inside a square root sign, you can take the pair out
and replace it with only one of the pair outside

Answer 2

in other words
\[ \sqrt{3\cdot 2 \cdot 2}= 2 \sqrt{3}\]
we take the 2*2 out of the square root, and put only 1 of the twos out front
we leave the 3 inside because there is only one 3 and we need a pair of 3's to take them out