Square Root Calculator › Square root of 550
Square Root of 550
√550 ≈ 23.452079
550 is not a perfect square, so √550 is an irrational number that is approximately 23.452079. In simplified radical form, √550 = 5√22.
√550 lies between √529 = 23 and √576 = 24.
| Number | 550 |
| Square root (decimal) | 23.452079 |
| Simplified radical | 5√22 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 550
550 = 2 × 5^2 × 11. This is what determines the simplified radical: for √550 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √550 = 5√22.
Estimating √550 by hand
√550 falls between √529 = 23 and √576 = 24, so it starts at 23.something. The Babylonian method refines that guess by averaging it with 550 ÷ the guess:
| Step | Estimate |
| Start | 23 |
| Step 1 | 23.456522 |
| Step 2 | 23.452079 |
| Step 3 | 23.452079 |
After 3 steps the estimate is 23.452079, matching √550 ≈ 23.452079.
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Frequently asked questions
Is 550 a perfect square?
No, 550 is not a perfect square, so its square root is irrational and approximately 23.452079.
What is the square root of 550 in simplest radical form?
√550 = 5√22 in simplest radical form.