Square Root Calculator › Square root of 215
Square Root of 215
√215 ≈ 14.662878
215 is not a perfect square, so √215 is an irrational number that is approximately 14.662878. In simplified radical form, √215 = √215.
√215 lies between √196 = 14 and √225 = 15.
| Number | 215 |
| Square root (decimal) | 14.662878 |
| Simplified radical | √215 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 215
215 = 5 × 43. This is what determines the simplified radical: for √215 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √215 is already in simplest radical form as √215.
Estimating √215 by hand
√215 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 215 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.678571 |
| Step 2 | 14.662887 |
| Step 3 | 14.662878 |
After 3 steps the estimate is 14.662878, matching √215 ≈ 14.662878.
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Frequently asked questions
Is 215 a perfect square?
No, 215 is not a perfect square, so its square root is irrational and approximately 14.662878.
What is the square root of 215 in simplest radical form?
√215 = √215 in simplest radical form.