Square Root Calculator › Square root of 410
Square Root of 410
√410 ≈ 20.248457
410 is not a perfect square, so √410 is an irrational number that is approximately 20.248457. In simplified radical form, √410 = √410.
√410 lies between √400 = 20 and √441 = 21.
| Number | 410 |
| Square root (decimal) | 20.248457 |
| Simplified radical | √410 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 410
410 = 2 × 5 × 41. This is what determines the simplified radical: for √410 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √410 is already in simplest radical form as √410.
Estimating √410 by hand
√410 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 410 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.25 |
| Step 2 | 20.248457 |
| Step 3 | 20.248457 |
After 3 steps the estimate is 20.248457, matching √410 ≈ 20.248457.
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Frequently asked questions
Is 410 a perfect square?
No, 410 is not a perfect square, so its square root is irrational and approximately 20.248457.
What is the square root of 410 in simplest radical form?
√410 = √410 in simplest radical form.