Square Root Calculator › Square root of 69
Square Root of 69
√69 ≈ 8.306624
69 is not a perfect square, so √69 is an irrational number that is approximately 8.306624. In simplified radical form, √69 = √69.
√69 lies between √64 = 8 and √81 = 9.
| Number | 69 |
| Square root (decimal) | 8.306624 |
| Simplified radical | √69 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 69
69 = 3 × 23. This is what determines the simplified radical: for √69 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √69 is already in simplest radical form as √69.
Estimating √69 by hand
√69 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 69 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.3125 |
| Step 2 | 8.306626 |
| Step 3 | 8.306624 |
After 3 steps the estimate is 8.306624, matching √69 ≈ 8.306624.
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Frequently asked questions
Is 69 a perfect square?
No, 69 is not a perfect square, so its square root is irrational and approximately 8.306624.
What is the square root of 69 in simplest radical form?
√69 = √69 in simplest radical form.