Square Root Calculator › Square root of 383
Square Root of 383
√383 ≈ 19.570386
383 is not a perfect square, so √383 is an irrational number that is approximately 19.570386. In simplified radical form, √383 = √383.
√383 lies between √361 = 19 and √400 = 20.
| Number | 383 |
| Square root (decimal) | 19.570386 |
| Simplified radical | √383 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 383
383 = 383. This is what determines the simplified radical: for √383 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √383 is already in simplest radical form as √383.
Estimating √383 by hand
√383 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 383 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.578947 |
| Step 2 | 19.570388 |
| Step 3 | 19.570386 |
After 3 steps the estimate is 19.570386, matching √383 ≈ 19.570386.
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Frequently asked questions
Is 383 a perfect square?
No, 383 is not a perfect square, so its square root is irrational and approximately 19.570386.
What is the square root of 383 in simplest radical form?
√383 = √383 in simplest radical form.