Square Root Calculator › Square root of 354
Square Root of 354
√354 ≈ 18.814888
354 is not a perfect square, so √354 is an irrational number that is approximately 18.814888. In simplified radical form, √354 = √354.
√354 lies between √324 = 18 and √361 = 19.
| Number | 354 |
| Square root (decimal) | 18.814888 |
| Simplified radical | √354 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 354
354 = 2 × 3 × 59. This is what determines the simplified radical: for √354 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √354 is already in simplest radical form as √354.
Estimating √354 by hand
√354 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 354 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.833333 |
| Step 2 | 18.814897 |
| Step 3 | 18.814888 |
After 3 steps the estimate is 18.814888, matching √354 ≈ 18.814888.
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Frequently asked questions
Is 354 a perfect square?
No, 354 is not a perfect square, so its square root is irrational and approximately 18.814888.
What is the square root of 354 in simplest radical form?
√354 = √354 in simplest radical form.