Square Root Calculator › Square root of 418
Square Root of 418
√418 ≈ 20.445048
418 is not a perfect square, so √418 is an irrational number that is approximately 20.445048. In simplified radical form, √418 = √418.
√418 lies between √400 = 20 and √441 = 21.
| Number | 418 |
| Square root (decimal) | 20.445048 |
| Simplified radical | √418 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 418
418 = 2 × 11 × 19. This is what determines the simplified radical: for √418 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √418 is already in simplest radical form as √418.
Estimating √418 by hand
√418 falls between √400 = 20 and √441 = 21, so it starts at 20.something. The Babylonian method refines that guess by averaging it with 418 ÷ the guess:
| Step | Estimate |
| Start | 20 |
| Step 1 | 20.45 |
| Step 2 | 20.445049 |
| Step 3 | 20.445048 |
After 3 steps the estimate is 20.445048, matching √418 ≈ 20.445048.
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Frequently asked questions
Is 418 a perfect square?
No, 418 is not a perfect square, so its square root is irrational and approximately 20.445048.
What is the square root of 418 in simplest radical form?
√418 = √418 in simplest radical form.