To rationalize the denominator of the expression 30/5√3−3√5, we need to eliminate the radical from the denominator.




To eliminate the radical from the denominator, we need to multiply both the numerator and denominator by the conjugate of the denominator. In this case, the conjugate of 5√3−3√5 is 5√3+3√5. So, we multiply both the numerator and denominator by 5√3+3√5:

30(5√3+3√5)
______________
(5√3−3√5)(5√3+3√5)


Now, we need to simplify the expression. When we multiply the denominator using the difference of squares, we get:

(5√3−3√5)(5√3+3√5) = (5√3)2 − (3√5)2 = 75 − 45 = 30

So, the expression simplifies to:

30(5√3+3√5)
______________
30


Now, we can cancel out the common factor of 30 in the numerator and denominator:

(5√3+3√5)
________
1


Therefore, the rationalized form of the expression 30/5√3−3√5 is (5√3+3√5).