Square Root Calculator › Square root of 26
Square Root of 26
√26 ≈ 5.09902
26 is not a perfect square, so √26 is an irrational number that is approximately 5.09902. In simplified radical form, √26 = √26.
√26 lies between √25 = 5 and √36 = 6.
| Number | 26 |
| Square root (decimal) | 5.09902 |
| Simplified radical | √26 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 26
26 = 2 × 13. This is what determines the simplified radical: for √26 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √26 is already in simplest radical form as √26.
Estimating √26 by hand
√26 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 26 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 5.1 |
| Step 2 | 5.09902 |
| Step 3 | 5.09902 |
After 3 steps the estimate is 5.09902, matching √26 ≈ 5.09902.
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Frequently asked questions
Is 26 a perfect square?
No, 26 is not a perfect square, so its square root is irrational and approximately 5.09902.
What is the square root of 26 in simplest radical form?
√26 = √26 in simplest radical form.