Square Root Calculator › Square root of 181
Square Root of 181
√181 ≈ 13.453624
181 is not a perfect square, so √181 is an irrational number that is approximately 13.453624. In simplified radical form, √181 = √181.
√181 lies between √169 = 13 and √196 = 14.
| Number | 181 |
| Square root (decimal) | 13.453624 |
| Simplified radical | √181 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 181
181 = 181. This is what determines the simplified radical: for √181 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √181 is already in simplest radical form as √181.
Estimating √181 by hand
√181 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 181 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.461538 |
| Step 2 | 13.453626 |
| Step 3 | 13.453624 |
After 3 steps the estimate is 13.453624, matching √181 ≈ 13.453624.
Nearby square roots
Frequently asked questions
Is 181 a perfect square?
No, 181 is not a perfect square, so its square root is irrational and approximately 13.453624.
What is the square root of 181 in simplest radical form?
√181 = √181 in simplest radical form.