Square Root Calculator › Square root of 395
Square Root of 395
√395 ≈ 19.874607
395 is not a perfect square, so √395 is an irrational number that is approximately 19.874607. In simplified radical form, √395 = √395.
√395 lies between √361 = 19 and √400 = 20.
| Number | 395 |
| Square root (decimal) | 19.874607 |
| Simplified radical | √395 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 395
395 = 5 × 79. This is what determines the simplified radical: for √395 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √395 is already in simplest radical form as √395.
Estimating √395 by hand
√395 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 395 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.894737 |
| Step 2 | 19.874617 |
| Step 3 | 19.874607 |
After 3 steps the estimate is 19.874607, matching √395 ≈ 19.874607.
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Frequently asked questions
Is 395 a perfect square?
No, 395 is not a perfect square, so its square root is irrational and approximately 19.874607.
What is the square root of 395 in simplest radical form?
√395 = √395 in simplest radical form.