Square Root Calculator › Square root of 23
Square Root of 23
√23 ≈ 4.795832
23 is not a perfect square, so √23 is an irrational number that is approximately 4.795832. In simplified radical form, √23 = √23.
√23 lies between √16 = 4 and √25 = 5.
| Number | 23 |
| Square root (decimal) | 4.795832 |
| Simplified radical | √23 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 23
23 = 23. This is what determines the simplified radical: for √23 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √23 is already in simplest radical form as √23.
Estimating √23 by hand
√23 falls between √16 = 4 and √25 = 5, so it starts at 4.something. The Babylonian method refines that guess by averaging it with 23 ÷ the guess:
| Step | Estimate |
| Start | 4 |
| Step 1 | 4.875 |
| Step 2 | 4.796474 |
| Step 3 | 4.795832 |
After 3 steps the estimate is 4.795832, matching √23 ≈ 4.795832.
Nearby square roots
Frequently asked questions
Is 23 a perfect square?
No, 23 is not a perfect square, so its square root is irrational and approximately 4.795832.
What is the square root of 23 in simplest radical form?
√23 = √23 in simplest radical form.