Question

How do you solve `(sqrt6) - sqrt(3/2)`?

Answer 1

Break the fraction under the square root sign into separate square roots, then find the common denominator and eventually get to `(sqrt(6))/2`

Explanation:

In order to subtract the fraction from the square root term, we need to have a common denominator.

Let's start with the given equation:

`sqrt(6)-sqrt(3/2)`

The key here is that the one term has a integer under the root sign and the other has a fraction. We can fix that by first taking the fraction under the square root and breaking it down into parts, like this:

`sqrt(6)-sqrt(3)/sqrt(2)`

And now we can multiply the first term by a creative form of 1 (i.e. `= sqrt(2)/sqrt(2)`) like so:

`(sqrt(6)*sqrt(2)/sqrt(2))-sqrt(3)/sqrt(2)`

`=sqrt(12)/sqrt(2)-sqrt(3)/sqrt(2)=(sqrt(12)-sqrt(3))/sqrt(2)=(2sqrt(3)-sqrt(3))/sqrt(2)=sqrt(3)/sqrt(2)`

And we can clean this up to get rid of the square root in the denominator:

`sqrt(3)/sqrt(2)*sqrt(2)/sqrt(2)=sqrt(6)/2`