Square Root Calculator › Square root of 66
Square Root of 66
√66 ≈ 8.124038
66 is not a perfect square, so √66 is an irrational number that is approximately 8.124038. In simplified radical form, √66 = √66.
√66 lies between √64 = 8 and √81 = 9.
| Number | 66 |
| Square root (decimal) | 8.124038 |
| Simplified radical | √66 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 66
66 = 2 × 3 × 11. This is what determines the simplified radical: for √66 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √66 is already in simplest radical form as √66.
Estimating √66 by hand
√66 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 66 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.125 |
| Step 2 | 8.124038 |
| Step 3 | 8.124038 |
After 3 steps the estimate is 8.124038, matching √66 ≈ 8.124038.
Nearby square roots
Frequently asked questions
Is 66 a perfect square?
No, 66 is not a perfect square, so its square root is irrational and approximately 8.124038.
What is the square root of 66 in simplest radical form?
√66 = √66 in simplest radical form.