Square Root Calculator › Square root of 217
Square Root of 217
√217 ≈ 14.73092
217 is not a perfect square, so √217 is an irrational number that is approximately 14.73092. In simplified radical form, √217 = √217.
√217 lies between √196 = 14 and √225 = 15.
| Number | 217 |
| Square root (decimal) | 14.73092 |
| Simplified radical | √217 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 217
217 = 7 × 31. This is what determines the simplified radical: for √217 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √217 is already in simplest radical form as √217.
Estimating √217 by hand
√217 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 217 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.75 |
| Step 2 | 14.730932 |
| Step 3 | 14.73092 |
After 3 steps the estimate is 14.73092, matching √217 ≈ 14.73092.
Nearby square roots
Frequently asked questions
Is 217 a perfect square?
No, 217 is not a perfect square, so its square root is irrational and approximately 14.73092.
What is the square root of 217 in simplest radical form?
√217 = √217 in simplest radical form.