Square Root Calculator › Square root of 104
Square Root of 104
√104 ≈ 10.198039
104 is not a perfect square, so √104 is an irrational number that is approximately 10.198039. In simplified radical form, √104 = 2√26.
√104 lies between √100 = 10 and √121 = 11.
| Number | 104 |
| Square root (decimal) | 10.198039 |
| Simplified radical | 2√26 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 104
104 = 2^3 × 13. This is what determines the simplified radical: for √104 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √104 = 2√26.
Estimating √104 by hand
√104 falls between √100 = 10 and √121 = 11, so it starts at 10.something. The Babylonian method refines that guess by averaging it with 104 ÷ the guess:
| Step | Estimate |
| Start | 10 |
| Step 1 | 10.2 |
| Step 2 | 10.198039 |
| Step 3 | 10.198039 |
After 3 steps the estimate is 10.198039, matching √104 ≈ 10.198039.
Nearby square roots
Frequently asked questions
Is 104 a perfect square?
No, 104 is not a perfect square, so its square root is irrational and approximately 10.198039.
What is the square root of 104 in simplest radical form?
√104 = 2√26 in simplest radical form.