Square Root Calculator › Square root of 219
Square Root of 219
√219 ≈ 14.798649
219 is not a perfect square, so √219 is an irrational number that is approximately 14.798649. In simplified radical form, √219 = √219.
√219 lies between √196 = 14 and √225 = 15.
| Number | 219 |
| Square root (decimal) | 14.798649 |
| Simplified radical | √219 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 219
219 = 3 × 73. This is what determines the simplified radical: for √219 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √219 is already in simplest radical form as √219.
Estimating √219 by hand
√219 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 219 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.821429 |
| Step 2 | 14.798666 |
| Step 3 | 14.798649 |
After 3 steps the estimate is 14.798649, matching √219 ≈ 14.798649.
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Frequently asked questions
Is 219 a perfect square?
No, 219 is not a perfect square, so its square root is irrational and approximately 14.798649.
What is the square root of 219 in simplest radical form?
√219 = √219 in simplest radical form.