Square Root Calculator › Square root of 28
Square Root of 28
√28 ≈ 5.291503
28 is not a perfect square, so √28 is an irrational number that is approximately 5.291503. In simplified radical form, √28 = 2√7.
√28 lies between √25 = 5 and √36 = 6.
| Number | 28 |
| Square root (decimal) | 5.291503 |
| Simplified radical | 2√7 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 28
28 = 2^2 × 7. This is what determines the simplified radical: for √28 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √28 = 2√7.
Estimating √28 by hand
√28 falls between √25 = 5 and √36 = 6, so it starts at 5.something. The Babylonian method refines that guess by averaging it with 28 ÷ the guess:
| Step | Estimate |
| Start | 5 |
| Step 1 | 5.3 |
| Step 2 | 5.291509 |
| Step 3 | 5.291503 |
After 3 steps the estimate is 5.291503, matching √28 ≈ 5.291503.
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Frequently asked questions
Is 28 a perfect square?
No, 28 is not a perfect square, so its square root is irrational and approximately 5.291503.
What is the square root of 28 in simplest radical form?
√28 = 2√7 in simplest radical form.