Write $\sqrt{\frac{16}{25}+\frac{9}{4}}$ as a common fraction.
The least common multiple of 25 and 4 is 100, so I can multiply the first fraction by $\frac{4}{4}$ and the second fraction by $\frac{25}{25}$ to get equivalent fractions with the same denominator. That gives me $\sqrt{\frac{64}{100}+\frac{225}{100}}$. Now I can add the fractions, since they have the same denominator. That gives me $\sqrt{\frac{64+225}{100}}=\sqrt{\frac{289}{100}}$. Now I can use the property that $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$, as long as both a and b are positive. That gives me $\frac{\sqrt{289}}{\sqrt{100}}$. I can simplify the square roots, since I know that 289 is a perfect square and 100 is a perfect square. That gives me $\frac{17}{10}$. This is already a common fraction, so I'm done. 