Square Root Calculator › Square root of 490
Square Root of 490
√490 ≈ 22.135944
490 is not a perfect square, so √490 is an irrational number that is approximately 22.135944. In simplified radical form, √490 = 7√10.
√490 lies between √484 = 22 and √529 = 23.
| Number | 490 |
| Square root (decimal) | 22.135944 |
| Simplified radical | 7√10 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 490
490 = 2 × 5 × 7^2. This is what determines the simplified radical: for √490 you pull out one copy of any prime that appears twice.
Here the paired factor 7 comes out from under the root, leaving √490 = 7√10.
Estimating √490 by hand
√490 falls between √484 = 22 and √529 = 23, so it starts at 22.something. The Babylonian method refines that guess by averaging it with 490 ÷ the guess:
| Step | Estimate |
| Start | 22 |
| Step 1 | 22.136364 |
| Step 2 | 22.135944 |
| Step 3 | 22.135944 |
After 3 steps the estimate is 22.135944, matching √490 ≈ 22.135944.
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Frequently asked questions
Is 490 a perfect square?
No, 490 is not a perfect square, so its square root is irrational and approximately 22.135944.
What is the square root of 490 in simplest radical form?
√490 = 7√10 in simplest radical form.