Chapter 6 - Radical Functions and Rational Exponents - 6-1 Roots and Radical Expressions - Practice and Problem-Solving Exercises - Page 364: 13

$-\dfrac{8}{13}$ and $\dfrac{8}{13}$

Note that $\left(\frac{8}{13}\right)^2=\frac{64}{169}$, so $\frac{8}{13}$ is a real square root of $\frac{64}{169}$, and $\left(-\frac{8}{13}\right)^2=\frac{64}{169}$, so $-\frac{8}{13}$ is a also real square root of $\frac{64}{169}$. Thus, the real square roots of $\frac{64}{169}$ are $-\frac{8}{13}$ and $\frac{8}{13}$.