Square Root Calculator › Square root of 353
Square Root of 353
√353 ≈ 18.788294
353 is not a perfect square, so √353 is an irrational number that is approximately 18.788294. In simplified radical form, √353 = √353.
√353 lies between √324 = 18 and √361 = 19.
| Number | 353 |
| Square root (decimal) | 18.788294 |
| Simplified radical | √353 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 353
353 = 353. This is what determines the simplified radical: for √353 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √353 is already in simplest radical form as √353.
Estimating √353 by hand
√353 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 353 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.805556 |
| Step 2 | 18.788302 |
| Step 3 | 18.788294 |
After 3 steps the estimate is 18.788294, matching √353 ≈ 18.788294.
Nearby square roots
Frequently asked questions
Is 353 a perfect square?
No, 353 is not a perfect square, so its square root is irrational and approximately 18.788294.
What is the square root of 353 in simplest radical form?
√353 = √353 in simplest radical form.