Square Root Calculator › Square root of 483
Square Root of 483
√483 ≈ 21.977261
483 is not a perfect square, so √483 is an irrational number that is approximately 21.977261. In simplified radical form, √483 = √483.
√483 lies between √441 = 21 and √484 = 22.
| Number | 483 |
| Square root (decimal) | 21.977261 |
| Simplified radical | √483 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 483
483 = 3 × 7 × 23. This is what determines the simplified radical: for √483 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √483 is already in simplest radical form as √483.
Estimating √483 by hand
√483 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 483 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 22 |
| Step 2 | 21.977273 |
| Step 3 | 21.977261 |
After 3 steps the estimate is 21.977261, matching √483 ≈ 21.977261.
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Frequently asked questions
Is 483 a perfect square?
No, 483 is not a perfect square, so its square root is irrational and approximately 21.977261.
What is the square root of 483 in simplest radical form?
√483 = √483 in simplest radical form.