Square Root Calculator › Square root of 387
Square Root of 387
√387 ≈ 19.672316
387 is not a perfect square, so √387 is an irrational number that is approximately 19.672316. In simplified radical form, √387 = 3√43.
√387 lies between √361 = 19 and √400 = 20.
| Number | 387 |
| Square root (decimal) | 19.672316 |
| Simplified radical | 3√43 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 387
387 = 3^2 × 43. This is what determines the simplified radical: for √387 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √387 = 3√43.
Estimating √387 by hand
√387 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 387 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.684211 |
| Step 2 | 19.672319 |
| Step 3 | 19.672316 |
After 3 steps the estimate is 19.672316, matching √387 ≈ 19.672316.
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Frequently asked questions
Is 387 a perfect square?
No, 387 is not a perfect square, so its square root is irrational and approximately 19.672316.
What is the square root of 387 in simplest radical form?
√387 = 3√43 in simplest radical form.