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.
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Hey Tanya, good to see you again. Here are the solutions for question 4: i) 402 Step 1: Find the largest perfect square less than 402 using the long division method. r 20 \\[-3pt] 2 ) 402 \\[-3pt] -4 00 \\[-3pt] 40 ) 02 \\[-3pt] -00 \\[-3pt] 2 The remainder is 2. This means 20^2 = 400. Step 2: The least number to be subtracted is the remainder. 402 - 400 = 2 Step 3: The square root of the perfect square obtained is 20. The least number to be subtracted is 2, and the square root of the perfect square is 20. ii) 1989 Step 1: Find the largest perfect square less than 1989 using the long division method. r 44 \\[-3pt] 4 ) 1989 \\[-3pt] -16 00 \\[-3pt] 84 ) 389 \\[-3pt] -336 \\[-3pt] 53 The remainder is 53. This means 44^2 = 1936. Step 2: The least number to be subtracted is the remainder. 1989 - 1936 = 53 Step 3: The square root of the perfect square obtained is 44. The least number to be subtracted is 53, and the square root of the perfect square is 44. iii) 3250 Step 1: Find the largest perfect square less than 3250 using the long division method. r 57 \\[-3pt] 5 ) 3250 \\[-3pt] -25 00 \\[-3pt] 107 ) 750 \\[-3pt] -749 \\[-3pt] 1 The remainder is 1. This means 57^2 = 3249. Step 2: The least number to be subtracted is the remainder. 3250 - 3249 = 1 Step 3: The square root of the perfect square obtained is 57. The least number to be subtracted is 1, and the square root of the perfect square is 57. iv) 825 Step 1: Find the largest perfect square less than 825 using the long division method. r 28 \\[-3pt] 2 ) 825 \\[-3pt] -4 00 \\[-3pt] 48 ) 425 \\[-3pt] -384 \\[-3pt] 41 The remainder is 41. This means 28^2 = 784. Step 2: The least number to be subtracted is the remainder. 825 - 784 = 41 Step 3: The square root of the perfect square obtained is 28. The least number to be subtracted is 41, and the square root of the perfect square is 28. v) 4000 Step 1: Find the largest perfect square less than 4000 using the long division method. r 63 \\[-3pt] 6 ) 4000 \\[-3pt] -36 00 \\[-3pt] 123 ) 400 \\[-3pt] -369 \\[-3pt] 31 The remainder is 31. This means 63^2 = 3969. Step 2: The least number to be subtracted is the remainder. 4000 - 3969 = 31 Step 3: The square root of the perfect square obtained is 63. The least number to be subtracted is 31, and the square root of the perfect square is 63. Send me the next one 📸