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. The problem states that there are 2304 mango trees in a garden. The number of trees in each row is equal to the total number of rows. We need to find the total number of rows. Let the number of rows be x. Since the number of trees in each row is also x, the total number of trees is x × x = x^2. So, we have the equation: x^2 = 2304 To find x, we need to calculate the square root of 2304. Step 2: Pair the digits of 2304 from the right. The pairs are (23) and (04). Step 3: Find the largest whole number whose square is less than or equal to the first pair, 23. 4^2 = 16 5^2 = 25 Since 16 < 23 and 25 > 23, the number is 4. Write 4 as the first digit of the square root. Step 4: Subtract 4^2 = 16 from 23. 23 - 16 = 7 Step 5: Bring down the next pair of digits, 04, next to the remainder. The new number is 704. Step 6: Double the current quotient (4 × 2 = 8). Write this as the new divisor's first digit. Now, find a digit 'x' such that when 'x' is placed next to 8 (forming 8x) and multiplied by 'x', the product is less than or equal to 704. Let's try x=8: 88 × 8 = 704 Step 7: Write 8 as the next digit in the square root. Subtract 704 from 704. 704 - 704 = 0 Since the remainder is 0 and there are no more pairs to bring down, the square root is 48. The total number of rows in the garden is 48. 3 done, 2 left today. You're making progress.