Square Root Calculator › Square root of 377
Square Root of 377
√377 ≈ 19.416488
377 is not a perfect square, so √377 is an irrational number that is approximately 19.416488. In simplified radical form, √377 = √377.
√377 lies between √361 = 19 and √400 = 20.
| Number | 377 |
| Square root (decimal) | 19.416488 |
| Simplified radical | √377 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 377
377 = 13 × 29. This is what determines the simplified radical: for √377 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √377 is already in simplest radical form as √377.
Estimating √377 by hand
√377 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 377 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.421053 |
| Step 2 | 19.416488 |
| Step 3 | 19.416488 |
After 3 steps the estimate is 19.416488, matching √377 ≈ 19.416488.
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Frequently asked questions
Is 377 a perfect square?
No, 377 is not a perfect square, so its square root is irrational and approximately 19.416488.
What is the square root of 377 in simplest radical form?
√377 = √377 in simplest radical form.