Study Guides/Maths/Square Root of 44100 by Long Division Method
Study Guide · Maths

Square Root of 44100 by Long Division Method

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.

Question (Click to Flip)

What is the square root of 44100?

Answer

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 ✓.

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Key Facts

√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.

Square Root by Prime Factorisation

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

Square Root by Long Division Method

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 ✓

Questions and Answers

What is the square root of 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 ✓.

How to find square root of 44100 by prime factorisation?+

Factorise: 44100 = 4 × 9 × 25 × 49 = 2²×3²×5²×7². Take one factor from each pair: 2×3×5×7 = 210. So √44100 = 210.

Is 44100 a perfect square?+

Yes. 44100 = 2²×3²×5²×7². All prime factors appear in pairs, so it is a perfect square. √44100 = 210.

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