Square Root Calculator › Square root of 388
Square Root of 388
√388 ≈ 19.697716
388 is not a perfect square, so √388 is an irrational number that is approximately 19.697716. In simplified radical form, √388 = 2√97.
√388 lies between √361 = 19 and √400 = 20.
| Number | 388 |
| Square root (decimal) | 19.697716 |
| Simplified radical | 2√97 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 388
388 = 2^2 × 97. This is what determines the simplified radical: for √388 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √388 = 2√97.
Estimating √388 by hand
√388 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 388 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.710526 |
| Step 2 | 19.69772 |
| Step 3 | 19.697716 |
After 3 steps the estimate is 19.697716, matching √388 ≈ 19.697716.
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Frequently asked questions
Is 388 a perfect square?
No, 388 is not a perfect square, so its square root is irrational and approximately 19.697716.
What is the square root of 388 in simplest radical form?
√388 = 2√97 in simplest radical form.