1. The problem is to solve the equation $$\sqrt{x^2} = \sqrt{80}$$ for $x$. 2. Recall that $$\sqrt{x^2} = |x|$$, which means the square root of $x^2$ is the absolute value of $x$. 3. Therefore, the equation becomes $$|x| = \sqrt{80}$$. 4. Simplify $$\sqrt{80}$$: $$\sqrt{80} = \sqrt{16 \times 5} = \sqrt{16} \times \sqrt{5} = 4\sqrt{5}$$. 5. So, $$|x| = 4\sqrt{5}$$. 6. This means $$x = \pm 4\sqrt{5}$$. 7. Numerically, $$4\sqrt{5} \approx 4 \times 2.236 = 8.944$$. 8. Hence, the solutions are $$x \approx \pm 8.944$$. 9. The value $x=8.9$ given is an approximation close to $8.944$. Final answer: $$x = \pm 4\sqrt{5} \approx \pm 8.944$$.