Can you help me explain my daughter on square root division on non explained numbers?

my daughter has a homework problem that looks like square root x - square root y over square root x + square root y





she also has a problem that looks like this a^2-49 over (p+7)^2 seems to be similar problems that I cant explain can anyone help me?Can you help me explain my daughter on square root division on non explained numbers?
sqrtx - sqrt y


-------------------


sqrtx + sqrt y ==%26gt; mutliply by the conjugate of denominator : sqrtx - sqrty





(sqrtx - sqrty) (sqrtx - sqrt y)


--------------------------------------鈥?br>

(sqrtx + sqrty) ( sqrtx - sqrt y)





denominator simplifies if you FOIL:





(sqrtx-sqrty)^2


--------------------


x - y





______________________________________鈥?br>




a^2 - 49 ======%26gt; factors as the difference of perfect squares


---------


(a+7)^2





(a-7)(a+7)


--------------


(a+7)(a+7)





a-7


-----


a+7





EDIT: Square roots and radicals are basically the same thing!


=]