Square Root Calculator › Square root of 86
Square Root of 86
√86 ≈ 9.273618
86 is not a perfect square, so √86 is an irrational number that is approximately 9.273618. In simplified radical form, √86 = √86.
√86 lies between √81 = 9 and √100 = 10.
| Number | 86 |
| Square root (decimal) | 9.273618 |
| Simplified radical | √86 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 86
86 = 2 × 43. This is what determines the simplified radical: for √86 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √86 is already in simplest radical form as √86.
Estimating √86 by hand
√86 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 86 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.277778 |
| Step 2 | 9.273619 |
| Step 3 | 9.273618 |
After 3 steps the estimate is 9.273618, matching √86 ≈ 9.273618.
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Frequently asked questions
Is 86 a perfect square?
No, 86 is not a perfect square, so its square root is irrational and approximately 9.273618.
What is the square root of 86 in simplest radical form?
√86 = √86 in simplest radical form.