Convert decimal number $1.2$ to fraction $\frac{12}{10}$. Reduce the fraction $\frac{12}{10}$ to lowest terms by extracting and canceling out $2$.
$$\sqrt{\frac{16}{3}+\frac{6}{5}}$$
Least common multiple of $3$ and $5$ is $15$. Convert $\frac{16}{3}$ and $\frac{6}{5}$ to fractions with denominator $15$.
$$\sqrt{\frac{80}{15}+\frac{18}{15}}$$
Since $\frac{80}{15}$ and $\frac{18}{15}$ have the same denominator, add them by adding their numerators.
$$\sqrt{\frac{80+18}{15}}$$
Add $80$ and $18$ to get $98$.
$$\sqrt{\frac{98}{15}}$$
Rewrite the square root of the division $\sqrt{\frac{98}{15}}$ as the division of square roots $\frac{\sqrt{98}}{\sqrt{15}}$.
$$\frac{\sqrt{98}}{\sqrt{15}}$$
Factor $98=7^{2}\times 2$. Rewrite the square root of the product $\sqrt{7^{2}\times 2}$ as the product of square roots $\sqrt{7^{2}}\sqrt{2}$. Take the square root of $7^{2}$.
$$\frac{7\sqrt{2}}{\sqrt{15}}$$
Rationalize the denominator of $\frac{7\sqrt{2}}{\sqrt{15}}$ by multiplying numerator and denominator by $\sqrt{15}$.
