This computer science problem involves algorithmic thinking and programming concepts. The solution below explains the approach, logic, and implementation step by step.
ScanSolve AI Answer
Step 1: Check if 10112 is even. 10112 ÷ 2 = 5056 Step 2: Check if 5056 is even. 5056 ÷ 2 = 2528 Step 3: Check if 2528 is even. 2528 ÷ 2 = 1264 Step 4: Check if 1264 is even. 1264 ÷ 2 = 632 Step 5: Check if 632 is even. 632 ÷ 2 = 316 Step 6: Check if 316 is even. 316 ÷ 2 = 158 Step 7: Check if 158 is even. 158 ÷ 2 = 79 Step 8: 79 is a prime number (not divisible by 2, 3, 5, or 7). Prime factorization: 10112 = 2^7 × 79 Step 9: Rewrite for square root. sqrt(10112) = sqrt(2^7 × 79) = sqrt(2^6 × 2 × 79) = sqrt((2^3)^2 × 158) Step 10: Simplify. sqrt(10112) = 2^3 sqrt(158) = 8sqrt(158) 8sqrt(158)