1. The problem is to calculate the value of $5\sqrt{425}$, which means 5 times the square root of 425. 2. Recall the formula for multiplication with square roots: $a\sqrt{b} = \sqrt{a^2 \times b}$ if you want to simplify under one root, or simply multiply the number outside by the root value. 3. First, simplify $\sqrt{425}$. Factor 425 into prime factors: $425 = 25 \times 17$. 4. Since $25$ is a perfect square, $\sqrt{425} = \sqrt{25 \times 17} = \sqrt{25} \times \sqrt{17} = 5\sqrt{17}$. 5. Now multiply by 5: $5 \times 5\sqrt{17} = 25\sqrt{17}$. 6. Therefore, the simplified form of $5\sqrt{425}$ is $25\sqrt{17}$. 7. If you want a decimal approximation, $\sqrt{17} \approx 4.1231$, so $25 \times 4.1231 \approx 103.08$. Final answer: $25\sqrt{17}$ or approximately 103.08.