Rewrite the square root of the division $\frac{9}{25}$ as the division of square roots $\frac{\sqrt{9}}{\sqrt{25}}$. Take the square root of both numerator and denominator.
Reduce the fraction $\frac{3}{6}$ to lowest terms by extracting and canceling out $3$.
$$\frac{1}{2}+\sqrt{\frac{5\times 16+1}{16}}$$
Multiply $5$ and $16$ to get $80$.
$$\frac{1}{2}+\sqrt{\frac{80+1}{16}}$$
Add $80$ and $1$ to get $81$.
$$\frac{1}{2}+\sqrt{\frac{81}{16}}$$
Rewrite the square root of the division $\frac{81}{16}$ as the division of square roots $\frac{\sqrt{81}}{\sqrt{16}}$. Take the square root of both numerator and denominator.
$$\frac{1}{2}+\frac{9}{4}$$
Least common multiple of $2$ and $4$ is $4$. Convert $\frac{1}{2}$ and $\frac{9}{4}$ to fractions with denominator $4$.
$$\frac{2}{4}+\frac{9}{4}$$
Since $\frac{2}{4}$ and $\frac{9}{4}$ have the same denominator, add them by adding their numerators.
