Square Root Calculator › Square root of 222
Square Root of 222
√222 ≈ 14.899664
222 is not a perfect square, so √222 is an irrational number that is approximately 14.899664. In simplified radical form, √222 = √222.
√222 lies between √196 = 14 and √225 = 15.
| Number | 222 |
| Square root (decimal) | 14.899664 |
| Simplified radical | √222 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 222
222 = 2 × 3 × 37. This is what determines the simplified radical: for √222 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √222 is already in simplest radical form as √222.
Estimating √222 by hand
√222 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 222 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.928571 |
| Step 2 | 14.899692 |
| Step 3 | 14.899664 |
After 3 steps the estimate is 14.899664, matching √222 ≈ 14.899664.
Nearby square roots
Frequently asked questions
Is 222 a perfect square?
No, 222 is not a perfect square, so its square root is irrational and approximately 14.899664.
What is the square root of 222 in simplest radical form?
√222 = √222 in simplest radical form.