Square Root Calculator › Square root of 223
Square Root of 223
√223 ≈ 14.933185
223 is not a perfect square, so √223 is an irrational number that is approximately 14.933185. In simplified radical form, √223 = √223.
√223 lies between √196 = 14 and √225 = 15.
| Number | 223 |
| Square root (decimal) | 14.933185 |
| Simplified radical | √223 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 223
223 = 223. This is what determines the simplified radical: for √223 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √223 is already in simplest radical form as √223.
Estimating √223 by hand
√223 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 223 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.964286 |
| Step 2 | 14.933217 |
| Step 3 | 14.933185 |
After 3 steps the estimate is 14.933185, matching √223 ≈ 14.933185.
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Frequently asked questions
Is 223 a perfect square?
No, 223 is not a perfect square, so its square root is irrational and approximately 14.933185.
What is the square root of 223 in simplest radical form?
√223 = √223 in simplest radical form.