Square Root Calculator › Square root of 85
Square Root of 85
√85 ≈ 9.219544
85 is not a perfect square, so √85 is an irrational number that is approximately 9.219544. In simplified radical form, √85 = √85.
√85 lies between √81 = 9 and √100 = 10.
| Number | 85 |
| Square root (decimal) | 9.219544 |
| Simplified radical | √85 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 85
85 = 5 × 17. This is what determines the simplified radical: for √85 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √85 is already in simplest radical form as √85.
Estimating √85 by hand
√85 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 85 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.222222 |
| Step 2 | 9.219545 |
| Step 3 | 9.219544 |
After 3 steps the estimate is 9.219544, matching √85 ≈ 9.219544.
Nearby square roots
Frequently asked questions
Is 85 a perfect square?
No, 85 is not a perfect square, so its square root is irrational and approximately 9.219544.
What is the square root of 85 in simplest radical form?
√85 = √85 in simplest radical form.