Square Root Calculator › Square root of 67
Square Root of 67
√67 ≈ 8.185353
67 is not a perfect square, so √67 is an irrational number that is approximately 8.185353. In simplified radical form, √67 = √67.
√67 lies between √64 = 8 and √81 = 9.
| Number | 67 |
| Square root (decimal) | 8.185353 |
| Simplified radical | √67 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 67
67 = 67. This is what determines the simplified radical: for √67 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √67 is already in simplest radical form as √67.
Estimating √67 by hand
√67 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 67 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.1875 |
| Step 2 | 8.185353 |
| Step 3 | 8.185353 |
After 3 steps the estimate is 8.185353, matching √67 ≈ 8.185353.
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Frequently asked questions
Is 67 a perfect square?
No, 67 is not a perfect square, so its square root is irrational and approximately 8.185353.
What is the square root of 67 in simplest radical form?
√67 = √67 in simplest radical form.