Square Root Calculator › Square root of 461
Square Root of 461
√461 ≈ 21.470911
461 is not a perfect square, so √461 is an irrational number that is approximately 21.470911. In simplified radical form, √461 = √461.
√461 lies between √441 = 21 and √484 = 22.
| Number | 461 |
| Square root (decimal) | 21.470911 |
| Simplified radical | √461 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 461
461 = 461. This is what determines the simplified radical: for √461 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √461 is already in simplest radical form as √461.
Estimating √461 by hand
√461 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 461 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.47619 |
| Step 2 | 21.470911 |
| Step 3 | 21.470911 |
After 3 steps the estimate is 21.470911, matching √461 ≈ 21.470911.
Nearby square roots
Frequently asked questions
Is 461 a perfect square?
No, 461 is not a perfect square, so its square root is irrational and approximately 21.470911.
What is the square root of 461 in simplest radical form?
√461 = √461 in simplest radical form.