1. **Problem:** Solve the equation $x^2 = \frac{16}{169}$ using roots. 2. **Formula and rule:** To solve $x^2 = a$, use the square root as the inverse operation: $$x = \pm \sqrt{a}$$ 3. **Step-by-step solution:** 1. Start with the equation: $$x^2 = \frac{16}{169}$$ 2. Take the square root of both sides: $$\sqrt{x^2} = \sqrt{\frac{16}{169}}$$ 3. Simplify the left side using the property $\sqrt{x^2} = |x|$: $$|x| = \sqrt{\frac{16}{169}}$$ 4. Simplify the right side by taking the square root of numerator and denominator: $$|x| = \frac{\sqrt{16}}{\sqrt{169}} = \frac{4}{13}$$ 5. Therefore, $x$ can be positive or negative: $$x = \pm \frac{4}{13}$$ 4. **Final answer:** $$x = \frac{4}{13} \text{ or } x = -\frac{4}{13}$$ This method applies to all similar problems where the variable is squared and equals a positive fraction or number.