1. The problem is to find the value of $\sqrt{8704}$. 2. The square root of a number $x$ is a value $y$ such that $y^2 = x$. 3. To simplify $\sqrt{8704}$, we try to factor 8704 into perfect squares. 4. First, divide 8704 by 64 (since 64 is a perfect square): $$\frac{8704}{64} = 136$$ 5. So, $\sqrt{8704} = \sqrt{64 \times 136} = \sqrt{64} \times \sqrt{136} = 8 \times \sqrt{136}$. 6. Next, factor 136 to find perfect squares: $$136 = 4 \times 34$$ 7. Thus, $\sqrt{136} = \sqrt{4 \times 34} = \sqrt{4} \times \sqrt{34} = 2 \times \sqrt{34}$. 8. Substitute back: $$8 \times \sqrt{136} = 8 \times 2 \times \sqrt{34} = 16 \times \sqrt{34}$$ 9. Therefore, the simplified form is: $$\sqrt{8704} = 16 \sqrt{34}$$ 10. To approximate, since $\sqrt{34} \approx 5.8309519$, then: $$16 \times 5.8309519 \approx 93.295$$ Final answer: $\sqrt{8704} = 16 \sqrt{34} \approx 93.295$