Square Root Calculator › Square root of 220
Square Root of 220
√220 ≈ 14.832397
220 is not a perfect square, so √220 is an irrational number that is approximately 14.832397. In simplified radical form, √220 = 2√55.
√220 lies between √196 = 14 and √225 = 15.
| Number | 220 |
| Square root (decimal) | 14.832397 |
| Simplified radical | 2√55 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 220
220 = 2^2 × 5 × 11. This is what determines the simplified radical: for √220 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √220 = 2√55.
Estimating √220 by hand
√220 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 220 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.857143 |
| Step 2 | 14.832418 |
| Step 3 | 14.832397 |
After 3 steps the estimate is 14.832397, matching √220 ≈ 14.832397.
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Frequently asked questions
Is 220 a perfect square?
No, 220 is not a perfect square, so its square root is irrational and approximately 14.832397.
What is the square root of 220 in simplest radical form?
√220 = 2√55 in simplest radical form.