Square Root Calculator › Square root of 8
Square Root of 8
√8 ≈ 2.828427
8 is not a perfect square, so √8 is an irrational number that is approximately 2.828427. In simplified radical form, √8 = 2√2.
√8 lies between √4 = 2 and √9 = 3.
| Number | 8 |
| Square root (decimal) | 2.828427 |
| Simplified radical | 2√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 8
8 = 2^3. This is what determines the simplified radical: for √8 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √8 = 2√2.
Estimating √8 by hand
√8 falls between √4 = 2 and √9 = 3, so it starts at 2.something. The Babylonian method refines that guess by averaging it with 8 ÷ the guess:
| Step | Estimate |
| Start | 2 |
| Step 1 | 3 |
| Step 2 | 2.833333 |
| Step 3 | 2.828431 |
After 3 steps the estimate is 2.828431, matching √8 ≈ 2.828427.
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Frequently asked questions
Is 8 a perfect square?
No, 8 is not a perfect square, so its square root is irrational and approximately 2.828427.
What is the square root of 8 in simplest radical form?
√8 = 2√2 in simplest radical form.