The square root of 44100 is 210. This can be found by the long division method or by prime factorisation. By prime factorisation: 44100 = 2² × 3² × 5² × 7², so √44100 = 2 × 3 × 5 × 7 = 210.
√44100 = 210.
Prime factorisation: 44100 = 2² × 3² × 5² × 7².
√44100 = 2 × 3 × 5 × 7 = 210.
Verification: 210² = 44100 ✓.
44100 is a perfect square — all prime factors appear in pairs.
Step 1: Prime factorise 44100.
44100 ÷ 2 = 22050 22050 ÷ 2 = 11025 11025 ÷ 3 = 3675 3675 ÷ 3 = 1225 1225 ÷ 5 = 245 245 ÷ 5 = 49 49 ÷ 7 = 7 7 ÷ 7 = 1
44100 = 2² × 3² × 5² × 7²
Step 2: Pair up prime factors. √44100 = √(2² × 3² × 5² × 7²) = 2 × 3 × 5 × 7 = 210
Answer: √44100 = 210
Group digits in pairs from right: 4 | 41 | 00
Step 1: Largest square ≤ 4 → 2 (2²=4). Quotient: 2. Remainder: 4−4=0.
Step 2: Bring down next pair: 41. Divisor = 2×2=4 (double quotient). Trial: 4_×_ ≤ 41. 4×1=41 → digit is 1. New divisor: 41. Remainder: 41−41=0.
Step 3: Bring down next pair: 00. Divisor = 210×2=420. Trial: 420×0=0 ≤ 0. Digit = 0. Remainder: 0.
Quotient (answer) = 210.
√44100 = 210
Verification: 210 × 210 = 44100 ✓
The square root of 44100 is 210. By prime factorisation: 44100 = 2²×3²×5²×7², so √44100 = 2×3×5×7 = 210. Verification: 210² = 44100 ✓.
Factorise: 44100 = 4 × 9 × 25 × 49 = 2²×3²×5²×7². Take one factor from each pair: 2×3×5×7 = 210. So √44100 = 210.
Yes. 44100 = 2²×3²×5²×7². All prime factors appear in pairs, so it is a perfect square. √44100 = 210.
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