Square Root Calculator › Square root of 468
Square Root of 468
√468 ≈ 21.633308
468 is not a perfect square, so √468 is an irrational number that is approximately 21.633308. In simplified radical form, √468 = 6√13.
√468 lies between √441 = 21 and √484 = 22.
| Number | 468 |
| Square root (decimal) | 21.633308 |
| Simplified radical | 6√13 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 468
468 = 2^2 × 3^2 × 13. This is what determines the simplified radical: for √468 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √468 = 6√13.
Estimating √468 by hand
√468 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 468 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.642857 |
| Step 2 | 21.63331 |
| Step 3 | 21.633308 |
After 3 steps the estimate is 21.633308, matching √468 ≈ 21.633308.
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Frequently asked questions
Is 468 a perfect square?
No, 468 is not a perfect square, so its square root is irrational and approximately 21.633308.
What is the square root of 468 in simplest radical form?
√468 = 6√13 in simplest radical form.