$$ \sqrt{\frac{45}{4}} $$ Simplify the expression

$\sqrt{\frac{45}{4}}$ can be simplified as follows:

First, we can simplify the fraction $\frac{45}{4}$ by dividing the numerator and denominator by their greatest common divisor, which is 5. This gives us $\frac{9}{\frac{4}{5}}$.

Next, we can simplify the expression $\frac{4}{5}$ by multiplying the numerator and denominator by their reciprocal. This gives us $\frac{9}{\frac{4}{5}} = \frac{9 \cdot 5}{4} = \frac{45}{4}$.

Finally, we can take the square root of $\frac{45}{4}$. The square root of a fraction is equal to the square root of the numerator divided by the square root of the denominator. Therefore, $\sqrt{\frac{45}{4}} = \frac{\sqrt{45}}{\sqrt{4}}$.

The square root of 45 can be simplified as $\sqrt{45} = \sqrt{9 \cdot 5} = \sqrt{9} \cdot \sqrt{5} = 3 \cdot \sqrt{5}$.

The square root of 4 is equal to 2.

Therefore, $\sqrt{\frac{45}{4}} = \frac{\sqrt{45}}{\sqrt{4}} = \frac{3 \cdot \sqrt{5}}{2}$.