Use Roots to Solve Equations For Problems \( 8-11 \), solve the equation. \( \begin{array}{l}\text { 8. } a^{2}=100\end{array} \) \( \begin{array}{l}\text { 10. } b^{2}=144 \\ \text { 12. A square park has an area of } 8100 \text { square meters. } \\ \text { A. Write an equation that can be used to determine the side length } s \text {, in } \\ \text { meters, of the park. } \\ \text { B. Solve your equation, and interpret the solution. }\end{array} \) \( \begin{array}{l}\text { 11. } x^{2}=225\end{array} \)

To solve the equation \( a^{2} = 100 \), take the square root of both sides, yielding \( a = \pm10 \). This means \( a \) can be either 10 or -10, as squaring either will return 100. For \( b^{2} = 144 \), the same approach gives \( b = \pm12 \), meaning \( b \) can also be either 12 or -12. For the park's area, you can write the equation \( s^2 = 8100 \). Solving this gives \( s = \pm90 \). Since we're talking about a side length, you'd only consider the positive value, so the side length of the park is 90 meters. Imagine a rectangular area where you can play, picnic, or just relax – it's a big space to enjoy!