Square Root Calculator › Square root of 467
Square Root of 467
√467 ≈ 21.610183
467 is not a perfect square, so √467 is an irrational number that is approximately 21.610183. In simplified radical form, √467 = √467.
√467 lies between √441 = 21 and √484 = 22.
| Number | 467 |
| Square root (decimal) | 21.610183 |
| Simplified radical | √467 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 467
467 = 467. This is what determines the simplified radical: for √467 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √467 is already in simplest radical form as √467.
Estimating √467 by hand
√467 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 467 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.619048 |
| Step 2 | 21.610185 |
| Step 3 | 21.610183 |
After 3 steps the estimate is 21.610183, matching √467 ≈ 21.610183.
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Frequently asked questions
Is 467 a perfect square?
No, 467 is not a perfect square, so its square root is irrational and approximately 21.610183.
What is the square root of 467 in simplest radical form?
√467 = √467 in simplest radical form.