Square Root Calculator › Square root of 39
Square Root of 39
√39 ≈ 6.244998
39 is not a perfect square, so √39 is an irrational number that is approximately 6.244998. In simplified radical form, √39 = √39.
√39 lies between √36 = 6 and √49 = 7.
| Number | 39 |
| Square root (decimal) | 6.244998 |
| Simplified radical | √39 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 39
39 = 3 × 13. This is what determines the simplified radical: for √39 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √39 is already in simplest radical form as √39.
Estimating √39 by hand
√39 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 39 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.25 |
| Step 2 | 6.245 |
| Step 3 | 6.244998 |
After 3 steps the estimate is 6.244998, matching √39 ≈ 6.244998.
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Frequently asked questions
Is 39 a perfect square?
No, 39 is not a perfect square, so its square root is irrational and approximately 6.244998.
What is the square root of 39 in simplest radical form?
√39 = √39 in simplest radical form.