Square Root Calculator › Square root of 360
Square Root of 360
√360 ≈ 18.973666
360 is not a perfect square, so √360 is an irrational number that is approximately 18.973666. In simplified radical form, √360 = 6√10.
√360 lies between √324 = 18 and √361 = 19.
| Number | 360 |
| Square root (decimal) | 18.973666 |
| Simplified radical | 6√10 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 360
360 = 2^3 × 3^2 × 5. This is what determines the simplified radical: for √360 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √360 = 6√10.
Estimating √360 by hand
√360 falls between √324 = 18 and √361 = 19, so it starts at 18.something. The Babylonian method refines that guess by averaging it with 360 ÷ the guess:
| Step | Estimate |
| Start | 18 |
| Step 1 | 19 |
| Step 2 | 18.973684 |
| Step 3 | 18.973666 |
After 3 steps the estimate is 18.973666, matching √360 ≈ 18.973666.
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Frequently asked questions
Is 360 a perfect square?
No, 360 is not a perfect square, so its square root is irrational and approximately 18.973666.
What is the square root of 360 in simplest radical form?
√360 = 6√10 in simplest radical form.