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.