Square Root Calculator › Square root of 448
Square Root of 448
√448 ≈ 21.16601
448 is not a perfect square, so √448 is an irrational number that is approximately 21.16601. In simplified radical form, √448 = 8√7.
√448 lies between √441 = 21 and √484 = 22.
| Number | 448 |
| Square root (decimal) | 21.16601 |
| Simplified radical | 8√7 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 448
448 = 2^6 × 7. This is what determines the simplified radical: for √448 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √448 = 8√7.
Estimating √448 by hand
√448 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 448 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.166667 |
| Step 2 | 21.16601 |
| Step 3 | 21.16601 |
After 3 steps the estimate is 21.16601, matching √448 ≈ 21.16601.
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Frequently asked questions
Is 448 a perfect square?
No, 448 is not a perfect square, so its square root is irrational and approximately 21.16601.
What is the square root of 448 in simplest radical form?
√448 = 8√7 in simplest radical form.