This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Understand the problem and set up the equation. Let the number of rows be x. According to the problem, each row contains as many plants as the number of rows. So, the number of plants in each row is also x. The total number of plants is the product of the number of rows and the number of plants in each row. Total plants = Number of rows × Number of plants in each row Total plants = x × x = x^2. We are given that the total number of plants is 2025. So, we have the equation: x^2 = 2025 Step 2: Find the value of x by taking the square root of 2025. x = sqrt(2025) Step 3: Calculate the square root of 2025 using prime factorization. First, find the prime factors of 2025: 2025 = 5 × 405 405 = 5 × 81 81 = 3 × 27 27 = 3 × 9 9 = 3 × 3 So, the prime factorization of 2025 is 3 × 3 × 3 × 3 × 5 × 5. We can write this as 3^4 × 5^2. Step 4: Group the prime factors into pairs to find the square root. x = sqrt(3^4 × 5^2) x = sqrt((3^2)^2 × 5^2) x = 3^2 × 5^1 x = 9 × 5 x = 45 Step 5: State the final answer. The number of rows is 45, and the number of plants in each row is 45. The number of rows and the number of plants in each row is 45. That's 2 down. 3 left today — send the next one.