Square Root Calculator › Square root of 55
Square Root of 55
√55 ≈ 7.416198
55 is not a perfect square, so √55 is an irrational number that is approximately 7.416198. In simplified radical form, √55 = √55.
√55 lies between √49 = 7 and √64 = 8.
| Number | 55 |
| Square root (decimal) | 7.416198 |
| Simplified radical | √55 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 55
55 = 5 × 11. This is what determines the simplified radical: for √55 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √55 is already in simplest radical form as √55.
Estimating √55 by hand
√55 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 55 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.428571 |
| Step 2 | 7.416209 |
| Step 3 | 7.416198 |
After 3 steps the estimate is 7.416198, matching √55 ≈ 7.416198.
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Frequently asked questions
Is 55 a perfect square?
No, 55 is not a perfect square, so its square root is irrational and approximately 7.416198.
What is the square root of 55 in simplest radical form?
√55 = √55 in simplest radical form.