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: Identify the given information. The area of the squared seminar hall (A) is 729 m^2. Step 2: Recall the formula for the side length of a square. For a square, the area (A) is equal to the side length (s) squared (A = s^2). To find the side length, we take the square root of the area: s = sqrt(A) Step 3: Substitute the given area into the formula. s = sqrt(729 m)^2 Step 4: Calculate the square root of 729 using the long division method. First, group the digits of 729 in pairs from the right: 7 29. Find the largest number whose square is less than or equal to the first group (7). 2^2 = 4, which is less than 7. 3^2 = 9, which is greater than 7. So, the first digit of the square root is 2. r 2 \\[-3pt] 2 | 7 \ 29 \\[-3pt] -4 29 \\[-3pt] 3 29 Bring down the next pair of digits (29) to the remainder (3), making it 329. Double the current quotient (2), which is 2 × 2 = 4. Write 4 as the first digit of the new divisor. Find the next digit for the divisor and quotient. We need a digit x such that 4x × x is less than or equal to 329. Let's try x=7: 47 × 7 = 329. r 2 \ 7 \\[-3pt] 2 | 7 \ 29 \\[-3pt] -4 29 \\[-3pt] 47 | 3 \ 29 \\[-3pt] -3 \ 29 \\[-3pt] 0 The remainder is 0, so the square root of 729 is 27. Step 5: State the length of the seminar hall. s = 27 m The length of the seminar hall is: 27 m You're doing great! What's next?