Square Root Calculator › Square root of 365
Square Root of 365
√365 ≈ 19.104973
365 is not a perfect square, so √365 is an irrational number that is approximately 19.104973. In simplified radical form, √365 = √365.
√365 lies between √361 = 19 and √400 = 20.
| Number | 365 |
| Square root (decimal) | 19.104973 |
| Simplified radical | √365 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 365
365 = 5 × 73. This is what determines the simplified radical: for √365 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √365 is already in simplest radical form as √365.
Estimating √365 by hand
√365 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 365 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.105263 |
| Step 2 | 19.104973 |
| Step 3 | 19.104973 |
After 3 steps the estimate is 19.104973, matching √365 ≈ 19.104973.
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Frequently asked questions
Is 365 a perfect square?
No, 365 is not a perfect square, so its square root is irrational and approximately 19.104973.
What is the square root of 365 in simplest radical form?
√365 = √365 in simplest radical form.