Square Root Calculator › Square root of 489
Square Root of 489
√489 ≈ 22.113344
489 is not a perfect square, so √489 is an irrational number that is approximately 22.113344. In simplified radical form, √489 = √489.
√489 lies between √484 = 22 and √529 = 23.
| Number | 489 |
| Square root (decimal) | 22.113344 |
| Simplified radical | √489 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 489
489 = 3 × 163. This is what determines the simplified radical: for √489 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √489 is already in simplest radical form as √489.
Estimating √489 by hand
√489 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 489 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.113636 |
| Step 2 | 22.113344 |
| Step 3 | 22.113344 |
After 3 steps the estimate is 22.113344, matching √489 ≈ 22.113344.
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Frequently asked questions
Is 489 a perfect square?
No, 489 is not a perfect square, so its square root is irrational and approximately 22.113344.
What is the square root of 489 in simplest radical form?
√489 = √489 in simplest radical form.