1. **Stating the problem:** We need to simplify each square root expression given in Part 4. 2. **Formula and rules:** The square root function \(\sqrt{x}\) gives the non-negative number whose square is \(x\). Important rules: - \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\) - \(\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}\) - \(\sqrt{a^2} = |a|\) - Simplify inside the root first if possible. 3. **Step-by-step solutions:** **4 a.** \(\sqrt{125} - 25\) - Simplify \(\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}\) - So expression is \(5\sqrt{5} - 25\) - This cannot be simplified further since terms are unlike. **4 b.** \(\sqrt{44^2}\) - Using \(\sqrt{a^2} = |a|\), \(\sqrt{44^2} = 44\) **4 c.** \(\sqrt{25} \times \sqrt{100}\) - Simplify each root: \(\sqrt{25} = 5\), \(\sqrt{100} = 10\) - Multiply: \(5 \times 10 = 50\) 4. **Final answers:** - 4 a: \(5\sqrt{5} - 25\) - 4 b: \(44\) - 4 c: \(50\)