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 5: i) 525 Step 1: Find the largest perfect square less than 525 using the long division method. r 22 \\[-3pt] 2 ) 525 \\[-3pt] -4 00 \\[-3pt] 42 ) 125 \\[-3pt] -84 \\[-3pt] 41 The quotient is 22, and the remainder is 41. This means 22^2 = 484. Step 2: The next perfect square is (22+1)^2 = 23^2 = 529. Step 3: The least number to be added is the difference between the next perfect square and the given number. 529 - 525 = 4 Step 4: The square root of the perfect square obtained is 23. The least number to be added is 4, and the square root of the perfect square is 23. ii) 1750 Step 1: Find the largest perfect square less than 1750 using the long division method. r 41 \\[-3pt] 4 ) 1750 \\[-3pt] -16 00 \\[-3pt] 81 ) 150 \\[-3pt] -81 \\[-3pt] 69 The quotient is 41, and the remainder is 69. This means 41^2 = 1681. Step 2: The next perfect square is (41+1)^2 = 42^2 = 1764. Step 3: The least number to be added is the difference between the next perfect square and the given number. 1764 - 1750 = 14 Step 4: The square root of the perfect square obtained is 42. The least number to be added is 14, and the square root of the perfect square is 42. iii) 252 Step 1: Find the largest perfect square less than 252 using the long division method. r 15 \\[-3pt] 1 ) 252 \\[-3pt] -1 00 \\[-3pt] 25 ) 152 \\[-3pt] -125 \\[-3pt] 27 The quotient is 15, and the remainder is 27. This means 15^2 = 225. Step 2: The next perfect square is (15+1)^2 = 16^2 = 256. Step 3: The least number to be added is the difference between the next perfect square and the given number. 256 - 252 = 4 Step 4: The square root of the perfect square obtained is 16. The least number to be added is 4, and the square root of the perfect square is 16. iv) 1825 Step 1: Find the largest perfect square less than 1825 using the long division method. r 42 \\[-3pt] 4 ) 1825 \\[-3pt] -16 00 \\[-3pt] 82 ) 225 \\[-3pt] -164 \\[-3pt] 61 The quotient is 42, and the remainder is 61. This means 42^2 = 1764. Step 2: The next perfect square is (42+1)^2 = 43^2 = 1849. Step 3: The least number to be added is the difference between the next perfect square and the given number. 1849 - 1825 = 24 Step 4: The square root of the perfect square obtained is 43. The least number to be added is 24, and the square root of the perfect square is 43. v) 6412 Step 1: Find the largest perfect square less than 6412 using the long division method. r 80 \\[-3pt] 8 ) 6412 \\[-3pt] -64 00 \\[-3pt] 160 ) 012 \\[-3pt] -000 \\[-3pt] 12 The quotient is 80, and the remainder is 12. This means 80^2 = 6400. Step 2: The next perfect square is (80+1)^2 = 81^2 = 6561. Step 3: The least number to be added is the difference between the next perfect square and the given number. 6561 - 6412 = 149 Step 4: The square root of the perfect square obtained is 81. The least number to be added is 149, and the square root of the perfect square is 81. 3 done, 2 left today. You're making progress.