Square Root Calculator › Square root of 479
Square Root of 479
√479 ≈ 21.886069
479 is not a perfect square, so √479 is an irrational number that is approximately 21.886069. In simplified radical form, √479 = √479.
√479 lies between √441 = 21 and √484 = 22.
| Number | 479 |
| Square root (decimal) | 21.886069 |
| Simplified radical | √479 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 479
479 = 479. This is what determines the simplified radical: for √479 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √479 is already in simplest radical form as √479.
Estimating √479 by hand
√479 falls between √441 = 21 and √484 = 22, so it starts at 21.something. The Babylonian method refines that guess by averaging it with 479 ÷ the guess:
| Step | Estimate |
| Start | 21 |
| Step 1 | 21.904762 |
| Step 2 | 21.886077 |
| Step 3 | 21.886069 |
After 3 steps the estimate is 21.886069, matching √479 ≈ 21.886069.
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Frequently asked questions
Is 479 a perfect square?
No, 479 is not a perfect square, so its square root is irrational and approximately 21.886069.
What is the square root of 479 in simplest radical form?
√479 = √479 in simplest radical form.