The perferct squares are 1, 4, 9. 16. 25, 36, etc.

The largest perfect square that will divide evenly 
into 24 is 4.  So write 24 as 4*6



The largest perfect square that will divide evenly 
into 18 is 9.  So write 18 as 9*2



Take individual square roots under the radicals:



We know that  and ,so





Multiply the 8 by the 15 outside the radicals an
multiply 6 by 2 underneath the radical:



The largest perfect square that will divide evenly 
into 12 is 4, so write 12 as 4 times 3 



Take individual square roots under the radical:



We know that , so we have





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2.  

Form the conjugate of the bottom.  That's the same
as the bottom with the sign of the second term changed.
So the conjugate of  is 
So put that over itself, as 

Now multiply the original expression by that:



Indicate the multiplication of the numerators and the denominators,
putting parentheses around those with two terms:



Distribute the top, and FOIL out the bottom:



Cancel the middle terms on the bottom:





When you square a square root you take away the radical:







Edwin