Square Root Calculator › Square root of 358
Square Root of 358
√358 ≈ 18.920888
358 is not a perfect square, so √358 is an irrational number that is approximately 18.920888. In simplified radical form, √358 = √358.
√358 lies between √324 = 18 and √361 = 19.
| Number | 358 |
| Square root (decimal) | 18.920888 |
| Simplified radical | √358 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 358
358 = 2 × 179. This is what determines the simplified radical: for √358 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √358 is already in simplest radical form as √358.
Estimating √358 by hand
√358 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 358 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 18.944444 |
| Step 2 | 18.920903 |
| Step 3 | 18.920888 |
After 3 steps the estimate is 18.920888, matching √358 ≈ 18.920888.
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Frequently asked questions
Is 358 a perfect square?
No, 358 is not a perfect square, so its square root is irrational and approximately 18.920888.
What is the square root of 358 in simplest radical form?
√358 = √358 in simplest radical form.