Square Root Calculator › Square root of 37
Square Root of 37
√37 ≈ 6.082763
37 is not a perfect square, so √37 is an irrational number that is approximately 6.082763. In simplified radical form, √37 = √37.
√37 lies between √36 = 6 and √49 = 7.
| Number | 37 |
| Square root (decimal) | 6.082763 |
| Simplified radical | √37 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 37
37 = 37. This is what determines the simplified radical: for √37 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √37 is already in simplest radical form as √37.
Estimating √37 by hand
√37 falls between √36 = 6 and √49 = 7, so it starts at 6.something. The Babylonian method refines that guess by averaging it with 37 ÷ the guess:
| Step | Estimate |
| Start | 6 |
| Step 1 | 6.083333 |
| Step 2 | 6.082763 |
| Step 3 | 6.082763 |
After 3 steps the estimate is 6.082763, matching √37 ≈ 6.082763.
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Frequently asked questions
Is 37 a perfect square?
No, 37 is not a perfect square, so its square root is irrational and approximately 6.082763.
What is the square root of 37 in simplest radical form?
√37 = √37 in simplest radical form.