What is the Square Root of 1000?

Instant answer with step-by-step solution

√1000 = 31.6227766017
√1000 = 31.6227766017
⚠ 1000 is not a perfect square — result rounded to 10 significant figures

Step-by-step explanation

  1. We need to find √1000 — a number that when multiplied by itself equals 1000.
  2. 1000 is not a perfect square. Its square root is irrational.
  3. It falls between √961 = 31 and √1024 = 32.
  4. Using the formula √N = N^(1/2): √1000 = 1000^0.5 = 31.6227766017
  5. Verification: 31.6227766017 × 31.6227766017 ≈ 1000 ✓ (rounded to 10 significant figures)

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Related calculations

Square root of 10001000 square root√999 = 31.6069612586√998 = 31.5911379979√997 = 31.5753068077√500 = 22.360679775√1 = 1√4 = 2

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Also see

Square Root Laws Square Root Chart Easiest Method Negative Square Roots