Square Root Calculator › Square root of 486
Square Root of 486
√486 ≈ 22.045408
486 is not a perfect square, so √486 is an irrational number that is approximately 22.045408. In simplified radical form, √486 = 9√6.
√486 lies between √484 = 22 and √529 = 23.
| Number | 486 |
| Square root (decimal) | 22.045408 |
| Simplified radical | 9√6 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 486
486 = 2 × 3^5. This is what determines the simplified radical: for √486 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √486 = 9√6.
Estimating √486 by hand
√486 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 486 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.045455 |
| Step 2 | 22.045408 |
| Step 3 | 22.045408 |
After 3 steps the estimate is 22.045408, matching √486 ≈ 22.045408.
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Frequently asked questions
Is 486 a perfect square?
No, 486 is not a perfect square, so its square root is irrational and approximately 22.045408.
What is the square root of 486 in simplest radical form?
√486 = 9√6 in simplest radical form.