3√20 + 2√45/4√5

To simplify the expression, we first need to simplify the square roots in the expression.

√20 can be simplified as √(4 * 5) = 2√5.

√45 can be simplified as √(9 * 5) = 3√5.

Replacing these simplified square roots in the expression, we have:

3√20 + 2√45 = 3(2√5) + 2(3√5)

= 6√5 + 6√5

= 12√5

Now, we need to simplify the expression 4√5.

Dividing both the numerator and denominator of 2√45 by 4, we get:

2√45/4 = (2/4) * √45 = (1/2) * √45.

Substituting this in the expression, we have:

12√5 + (1/2) * √45.

So, the simplified expression is:

12√5 + (1/2) * √45.