Square Root Calculator › Square root of 214
Square Root of 214
√214 ≈ 14.628739
214 is not a perfect square, so √214 is an irrational number that is approximately 14.628739. In simplified radical form, √214 = √214.
√214 lies between √196 = 14 and √225 = 15.
| Number | 214 |
| Square root (decimal) | 14.628739 |
| Simplified radical | √214 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 214
214 = 2 × 107. This is what determines the simplified radical: for √214 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √214 is already in simplest radical form as √214.
Estimating √214 by hand
√214 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 214 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.642857 |
| Step 2 | 14.628746 |
| Step 3 | 14.628739 |
After 3 steps the estimate is 14.628739, matching √214 ≈ 14.628739.
Nearby square roots
Frequently asked questions
Is 214 a perfect square?
No, 214 is not a perfect square, so its square root is irrational and approximately 14.628739.
What is the square root of 214 in simplest radical form?
√214 = √214 in simplest radical form.