How do you get 1 divided by the square root of 3 divided by 2?

Answer 1

You would go about this question by first specifying whether there are parenthesis around the square root (3/2) or if it looks like (square root 3)/2

Case A would look something like this. 1/(square root of 3/2)

in this case you would multiply both the top and bottom by (square root of 3/2). The bottom portion would become (surprisingly!) 3/2. the top portion would be left as (square root of 3/2). Then, because you are dividing by a fraction, the KEEP CHANGE FLIP rule applies. (square root of 3/2) divided by 3/2 would become (square root of 3/2) multiplied by 2/3 which = 2(square root of 3/2)/3. You can then say that 2 is equal to radical 4 and multiply this by the numerator of the other radical, to get radical 12/2 which equals radical 6. Radical 6 over 3 would be the simplified answer.

Case B would look something like this. 1/(square root 3)/2

In this case you would multiply both the top and the bottom by (square root of 3). You would get (square root of 3) divided by 3/2. Then KEEP CHANGE FLIP applies again, and it becomes (square root of 3) multiplied by 2/3. This would then equal 2 radical 3 over 3.