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
Here are the solutions for question 3: i) 2.56 Step 1: Group the digits in pairs from the decimal point. For 2.56, the pairs are 2 and 56. Step 2: Find the largest integer whose square is less than or equal to the first pair (2). This is 1 (1^2 = 1). Write 1 as the quotient and subtract 1 from 2. Step 3: Bring down the next pair (56) and place the decimal point in the quotient. The new dividend is 156. Double the current quotient (1) to get 2. Find a digit 'x' such that 2x × x 156. Here, 26 × 6 = 156. r 1.6 \\[-3pt] 1 ) 2.56 \\[-3pt] -1 .00 \\[-3pt] 26 ) 156 \\[-3pt] -156 \\[-3pt] 0 The square root of 2.56 is 1.6. ii) 7.29 Step 1: Group the digits in pairs from the decimal point. For 7.29, the pairs are 7 and 29. Step 2: Find the largest integer whose square is less than or equal to the first pair (7). This is 2 (2^2 = 4). Write 2 as the quotient and subtract 4 from 7. Step 3: Bring down the next pair (29) and place the decimal point in the quotient. The new dividend is 329. Double the current quotient (2) to get 4. Find a digit 'x' such that 4x × x 329. Here, 47 × 7 = 329. r 2.7 \\[-3pt] 2 ) 7.29 \\[-3pt] -4 .00 \\[-3pt] 47 ) 329 \\[-3pt] -329 \\[-3pt] 0 The square root of 7.29 is 2.7. iii) 51.84 Step 1: Group the digits in pairs from the decimal point. For 51.84, the pairs are 51 and 84. Step 2: Find the largest integer whose square is less than or equal to the first pair (51). This is 7 (7^2 = 49). Write 7 as the quotient and subtract 49 from 51. Step 3: Bring down the next pair (84) and place the decimal point in the quotient. The new dividend is 284. Double the current quotient (7) to get 14. Find a digit 'x' such that 14x × x 284. Here, 142 × 2 = 284. r 7.2 \\[-3pt] 7 ) 51.84 \\[-3pt] -49 .00 \\[-3pt] 142 ) 284 \\[-3pt] -284 \\[-3pt] 0 The square root of 51.84 is 7.2. v) 31.36 Step 1: Group the digits in pairs from the decimal point. For 31.36, the pairs are 31 and 36. Step 2: Find the largest integer whose square is less than or equal to the first pair (31). This is 5 (5^2 = 25). Write 5 as the quotient and subtract 25 from 31. Step 3: Bring down the next pair (36) and place the decimal point in the quotient. The new dividend is 636. Double the current quotient (5) to get 10. Find a digit 'x' such that 10x × x 636. Here, 106 × 6 = 636. r 5.6 \\[-3pt] 5 ) 31.36 \\[-3pt] -25 .00 \\[-3pt] 106 ) 636 \\[-3pt] -636 \\[-3pt] 0 The square root of 31.36 is 5.6. That's 2 down. 3 left today — send the next one.