To eliminate irrationality in the denominator, we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator.

Given that the denominator is √(√5 + 3), we can multiply both the numerator and the denominator by √(√5 + 3) to rationalize the denominator:

4/ √(√5 + 3) * √(√5 + 3) / √(√5 + 3)

This simplifies to:

4 * √(√5 + 3) / (√5 + 3)

So, the expression after rationalizing the denominator is:

4 * √(√5 + 3) / (√5 + 3)