Square Root Calculator › Square root of 480
Square Root of 480
√480 ≈ 21.908902
480 is not a perfect square, so √480 is an irrational number that is approximately 21.908902. In simplified radical form, √480 = 4√30.
√480 lies between √441 = 21 and √484 = 22.
| Number | 480 |
| Square root (decimal) | 21.908902 |
| Simplified radical | 4√30 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 480
480 = 2^5 × 3 × 5. This is what determines the simplified radical: for √480 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √480 = 4√30.
Estimating √480 by hand
√480 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 480 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.928571 |
| Step 2 | 21.908911 |
| Step 3 | 21.908902 |
After 3 steps the estimate is 21.908902, matching √480 ≈ 21.908902.
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Frequently asked questions
Is 480 a perfect square?
No, 480 is not a perfect square, so its square root is irrational and approximately 21.908902.
What is the square root of 480 in simplest radical form?
√480 = 4√30 in simplest radical form.