Square Root Calculator › Square root of 38
Square Root of 38
√38 ≈ 6.164414
38 is not a perfect square, so √38 is an irrational number that is approximately 6.164414. In simplified radical form, √38 = √38.
√38 lies between √36 = 6 and √49 = 7.
| Number | 38 |
| Square root (decimal) | 6.164414 |
| Simplified radical | √38 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 38
38 = 2 × 19. This is what determines the simplified radical: for √38 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √38 is already in simplest radical form as √38.
Estimating √38 by hand
√38 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 38 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.166667 |
| Step 2 | 6.164414 |
| Step 3 | 6.164414 |
After 3 steps the estimate is 6.164414, matching √38 ≈ 6.164414.
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Frequently asked questions
Is 38 a perfect square?
No, 38 is not a perfect square, so its square root is irrational and approximately 6.164414.
What is the square root of 38 in simplest radical form?
√38 = √38 in simplest radical form.