Square Root Calculator › Square root of 368
Square Root of 368
√368 ≈ 19.183326
368 is not a perfect square, so √368 is an irrational number that is approximately 19.183326. In simplified radical form, √368 = 4√23.
√368 lies between √361 = 19 and √400 = 20.
| Number | 368 |
| Square root (decimal) | 19.183326 |
| Simplified radical | 4√23 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 368
368 = 2^4 × 23. This is what determines the simplified radical: for √368 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √368 = 4√23.
Estimating √368 by hand
√368 falls between √361 = 19 and √400 = 20, so it starts at 19.something. The Babylonian method refines that guess by averaging it with 368 ÷ the guess:
| Step | Estimate |
| Start | 19 |
| Step 1 | 19.184211 |
| Step 2 | 19.183326 |
| Step 3 | 19.183326 |
After 3 steps the estimate is 19.183326, matching √368 ≈ 19.183326.
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Frequently asked questions
Is 368 a perfect square?
No, 368 is not a perfect square, so its square root is irrational and approximately 19.183326.
What is the square root of 368 in simplest radical form?
√368 = 4√23 in simplest radical form.