Square Root Calculator › Square root of 95
Square Root of 95
√95 ≈ 9.746794
95 is not a perfect square, so √95 is an irrational number that is approximately 9.746794. In simplified radical form, √95 = √95.
√95 lies between √81 = 9 and √100 = 10.
| Number | 95 |
| Square root (decimal) | 9.746794 |
| Simplified radical | √95 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 95
95 = 5 × 19. This is what determines the simplified radical: for √95 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √95 is already in simplest radical form as √95.
Estimating √95 by hand
√95 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 95 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.777778 |
| Step 2 | 9.746843 |
| Step 3 | 9.746794 |
After 3 steps the estimate is 9.746794, matching √95 ≈ 9.746794.
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Frequently asked questions
Is 95 a perfect square?
No, 95 is not a perfect square, so its square root is irrational and approximately 9.746794.
What is the square root of 95 in simplest radical form?
√95 = √95 in simplest radical form.