Square Root Calculator › Square root of 218
Square Root of 218
√218 ≈ 14.764823
218 is not a perfect square, so √218 is an irrational number that is approximately 14.764823. In simplified radical form, √218 = √218.
√218 lies between √196 = 14 and √225 = 15.
| Number | 218 |
| Square root (decimal) | 14.764823 |
| Simplified radical | √218 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 218
218 = 2 × 109. This is what determines the simplified radical: for √218 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √218 is already in simplest radical form as √218.
Estimating √218 by hand
√218 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 218 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.785714 |
| Step 2 | 14.764838 |
| Step 3 | 14.764823 |
After 3 steps the estimate is 14.764823, matching √218 ≈ 14.764823.
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Frequently asked questions
Is 218 a perfect square?
No, 218 is not a perfect square, so its square root is irrational and approximately 14.764823.
What is the square root of 218 in simplest radical form?
√218 = √218 in simplest radical form.