Square Root Calculator › Square root of 83
Square Root of 83
√83 ≈ 9.110434
83 is not a perfect square, so √83 is an irrational number that is approximately 9.110434. In simplified radical form, √83 = √83.
√83 lies between √81 = 9 and √100 = 10.
| Number | 83 |
| Square root (decimal) | 9.110434 |
| Simplified radical | √83 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 83
83 = 83. This is what determines the simplified radical: for √83 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √83 is already in simplest radical form as √83.
Estimating √83 by hand
√83 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 83 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.111111 |
| Step 2 | 9.110434 |
| Step 3 | 9.110434 |
After 3 steps the estimate is 9.110434, matching √83 ≈ 9.110434.
Nearby square roots
Frequently asked questions
Is 83 a perfect square?
No, 83 is not a perfect square, so its square root is irrational and approximately 9.110434.
What is the square root of 83 in simplest radical form?
√83 = √83 in simplest radical form.