Square Root Calculator › Square root of 61
Square Root of 61
√61 ≈ 7.81025
61 is not a perfect square, so √61 is an irrational number that is approximately 7.81025. In simplified radical form, √61 = √61.
√61 lies between √49 = 7 and √64 = 8.
| Number | 61 |
| Square root (decimal) | 7.81025 |
| Simplified radical | √61 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 61
61 = 61. This is what determines the simplified radical: for √61 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √61 is already in simplest radical form as √61.
Estimating √61 by hand
√61 falls between √49 = 7 and √64 = 8, so it starts at 7.something. The Babylonian method refines that guess by averaging it with 61 ÷ the guess:
| Step | Estimate |
| Start | 7 |
| Step 1 | 7.857143 |
| Step 2 | 7.81039 |
| Step 3 | 7.81025 |
After 3 steps the estimate is 7.81025, matching √61 ≈ 7.81025.
Nearby square roots
Frequently asked questions
Is 61 a perfect square?
No, 61 is not a perfect square, so its square root is irrational and approximately 7.81025.
What is the square root of 61 in simplest radical form?
√61 = √61 in simplest radical form.