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
You're on the right track with the long division method for sqrt(2304), but there's a small error in your calculation. Let's re-examine the steps. Here's the correct way to find the square root of 2304 using the long division method: Step 1: Pair the digits from the right: 23 \ 04. Step 2: Find the largest number whose square is less than or equal to 23. This is 4, since 4^2 = 16. Step 3: Write 4 as the first digit of the quotient. Subtract 16 from 23 to get 7. Bring down the next pair, 04, to make the new dividend 704. Step 4: Double the current quotient (4) to get 8. Now, we need to find a digit 'x' such that 8x × x 704. You correctly identified that the next digit in the quotient is 8, making the quotient 48. So, we calculate 88 × 8. 88 × 8 = 704. Step 5: Write 8 as the next digit in the quotient. Subtract 704 from 704 to get 0. Your mistake was in the multiplication and subtraction in Step 4. You wrote 64 instead of 704 when multiplying 88 × 8. Here's how the long division should look: r 48 \\[-3pt] 4 ) 23 \ 04 \\[-3pt] -16 \\[-3pt] 88 704 \\[-3pt] -704 \\[-3pt] 0 The square root of 2304 is 48. sqrt(2304) = 48 That's 2 down. 3 left today — send the next one.