Square Root Calculator › Square root of 364
Square Root of 364
√364 ≈ 19.078784
364 is not a perfect square, so √364 is an irrational number that is approximately 19.078784. In simplified radical form, √364 = 2√91.
√364 lies between √361 = 19 and √400 = 20.
| Number | 364 |
| Square root (decimal) | 19.078784 |
| Simplified radical | 2√91 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 364
364 = 2^2 × 7 × 13. This is what determines the simplified radical: for √364 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √364 = 2√91.
Estimating √364 by hand
√364 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 364 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.078947 |
| Step 2 | 19.078784 |
| Step 3 | 19.078784 |
After 3 steps the estimate is 19.078784, matching √364 ≈ 19.078784.
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Frequently asked questions
Is 364 a perfect square?
No, 364 is not a perfect square, so its square root is irrational and approximately 19.078784.
What is the square root of 364 in simplest radical form?
√364 = 2√91 in simplest radical form.