Square Root Calculator › Square root of 495
Square Root of 495
√495 ≈ 22.248595
495 is not a perfect square, so √495 is an irrational number that is approximately 22.248595. In simplified radical form, √495 = 3√55.
√495 lies between √484 = 22 and √529 = 23.
| Number | 495 |
| Square root (decimal) | 22.248595 |
| Simplified radical | 3√55 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 495
495 = 3^2 × 5 × 11. This is what determines the simplified radical: for √495 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √495 = 3√55.
Estimating √495 by hand
√495 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 495 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.25 |
| Step 2 | 22.248596 |
| Step 3 | 22.248595 |
After 3 steps the estimate is 22.248595, matching √495 ≈ 22.248595.
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Frequently asked questions
Is 495 a perfect square?
No, 495 is not a perfect square, so its square root is irrational and approximately 22.248595.
What is the square root of 495 in simplest radical form?
√495 = 3√55 in simplest radical form.