Square Root Calculator › Square root of 355
Square Root of 355
√355 ≈ 18.841444
355 is not a perfect square, so √355 is an irrational number that is approximately 18.841444. In simplified radical form, √355 = √355.
√355 lies between √324 = 18 and √361 = 19.
| Number | 355 |
| Square root (decimal) | 18.841444 |
| Simplified radical | √355 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 355
355 = 5 × 71. This is what determines the simplified radical: for √355 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √355 is already in simplest radical form as √355.
Estimating √355 by hand
√355 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 355 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.861111 |
| Step 2 | 18.841454 |
| Step 3 | 18.841444 |
After 3 steps the estimate is 18.841444, matching √355 ≈ 18.841444.
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Frequently asked questions
Is 355 a perfect square?
No, 355 is not a perfect square, so its square root is irrational and approximately 18.841444.
What is the square root of 355 in simplest radical form?
√355 = √355 in simplest radical form.