Square Root Calculator › Square root of 370
Square Root of 370
√370 ≈ 19.235384
370 is not a perfect square, so √370 is an irrational number that is approximately 19.235384. In simplified radical form, √370 = √370.
√370 lies between √361 = 19 and √400 = 20.
| Number | 370 |
| Square root (decimal) | 19.235384 |
| Simplified radical | √370 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 370
370 = 2 × 5 × 37. This is what determines the simplified radical: for √370 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √370 is already in simplest radical form as √370.
Estimating √370 by hand
√370 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 370 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.236842 |
| Step 2 | 19.235384 |
| Step 3 | 19.235384 |
After 3 steps the estimate is 19.235384, matching √370 ≈ 19.235384.
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Frequently asked questions
Is 370 a perfect square?
No, 370 is not a perfect square, so its square root is irrational and approximately 19.235384.
What is the square root of 370 in simplest radical form?
√370 = √370 in simplest radical form.