Square Root Calculator › Square root of 206
Square Root of 206
√206 ≈ 14.3527
206 is not a perfect square, so √206 is an irrational number that is approximately 14.3527. In simplified radical form, √206 = √206.
√206 lies between √196 = 14 and √225 = 15.
| Number | 206 |
| Square root (decimal) | 14.3527 |
| Simplified radical | √206 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 206
206 = 2 × 103. This is what determines the simplified radical: for √206 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √206 is already in simplest radical form as √206.
Estimating √206 by hand
√206 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 206 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.357143 |
| Step 2 | 14.352701 |
| Step 3 | 14.3527 |
After 3 steps the estimate is 14.3527, matching √206 ≈ 14.3527.
Nearby square roots
Frequently asked questions
Is 206 a perfect square?
No, 206 is not a perfect square, so its square root is irrational and approximately 14.3527.
What is the square root of 206 in simplest radical form?
√206 = √206 in simplest radical form.