Square Root Calculator › Square root of 295
Square Root of 295
√295 ≈ 17.175564
295 is not a perfect square, so √295 is an irrational number that is approximately 17.175564. In simplified radical form, √295 = √295.
√295 lies between √289 = 17 and √324 = 18.
| Number | 295 |
| Square root (decimal) | 17.175564 |
| Simplified radical | √295 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 295
295 = 5 × 59. This is what determines the simplified radical: for √295 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √295 is already in simplest radical form as √295.
Estimating √295 by hand
√295 falls between √289 = 17 and √324 = 18, so it starts at 17.something. The Babylonian method refines that guess by averaging it with 295 ÷ the guess:
| Step | Estimate |
| Start | 17 |
| Step 1 | 17.176471 |
| Step 2 | 17.175564 |
| Step 3 | 17.175564 |
After 3 steps the estimate is 17.175564, matching √295 ≈ 17.175564.
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Frequently asked questions
Is 295 a perfect square?
No, 295 is not a perfect square, so its square root is irrational and approximately 17.175564.
What is the square root of 295 in simplest radical form?
√295 = √295 in simplest radical form.