Square Root Calculator › Square root of 207
Square Root of 207
√207 ≈ 14.387495
207 is not a perfect square, so √207 is an irrational number that is approximately 14.387495. In simplified radical form, √207 = 3√23.
√207 lies between √196 = 14 and √225 = 15.
| Number | 207 |
| Square root (decimal) | 14.387495 |
| Simplified radical | 3√23 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 207
207 = 3^2 × 23. This is what determines the simplified radical: for √207 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √207 = 3√23.
Estimating √207 by hand
√207 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 207 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.392857 |
| Step 2 | 14.387496 |
| Step 3 | 14.387495 |
After 3 steps the estimate is 14.387495, matching √207 ≈ 14.387495.
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Frequently asked questions
Is 207 a perfect square?
No, 207 is not a perfect square, so its square root is irrational and approximately 14.387495.
What is the square root of 207 in simplest radical form?
√207 = 3√23 in simplest radical form.