Square Root Calculator › Square root of 216
Square Root of 216
√216 ≈ 14.696938
216 is not a perfect square, so √216 is an irrational number that is approximately 14.696938. In simplified radical form, √216 = 6√6.
√216 lies between √196 = 14 and √225 = 15.
| Number | 216 |
| Square root (decimal) | 14.696938 |
| Simplified radical | 6√6 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 216
216 = 2^3 × 3^3. This is what determines the simplified radical: for √216 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √216 = 6√6.
Estimating √216 by hand
√216 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 216 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.714286 |
| Step 2 | 14.696949 |
| Step 3 | 14.696938 |
After 3 steps the estimate is 14.696938, matching √216 ≈ 14.696938.
Nearby square roots
Frequently asked questions
Is 216 a perfect square?
No, 216 is not a perfect square, so its square root is irrational and approximately 14.696938.
What is the square root of 216 in simplest radical form?
√216 = 6√6 in simplest radical form.