Ok, by divide, I presume you are talking about rationalising the denominator.
For info on how to do this, check this site out: http://www.purplemath.com/modules/radicals5.htm
Ok, on to solving:
In the first one, notice how the problem can be rewritten as: (2*sqrt(3))/(2*sqrt(5)). This can be rewritten as (2/2)*(sqrt(3)/(sqrt(5))). Since 2/2 is just 1, we can rewrite the problem as
(1)*(sqrt(3)/(sqrt(5))), which is just (sqrt(3)/(sqrt(5))).
From here, we rationalise the denominator by multiplying the expression by sqrt(5)/sqrt(5). We can do this because sqrt(5)/sqrt(5) is simply 1, and multiplying something by 1 doesn't change the nature of the expression.
So our expression becomes: sqrt(3)/(sqrt(5))*sqrt(5)/sqrt(5), which simplifies to become sqrt(15)/5. Since sqrt(15) is not something we can simplify, our final answer remains sqrt(15)/5.
Now for the second problem, the procedure is basically the same.
We multiply the expression by sqrt(10)/sqrt(10), so we get: sqrt(5)/sqrt(10)*sqrt(10)/sqrt(10), which simplifies to become sqrt(50)/sqrt(100).
Since sqrt(100) simplifies to 10, the expression can be simplified to read: sqrt(50)/10.
Now unlike the last problem, this numerator can be simplified, as it is a multiple of 25. sqrt(50)=5sqrt(2)
So our expression reads (5sqrt(2))/10, which can be simplified to sqrt(2)/2 for our final answer.
