Square Root Calculator › Square root of 76
Square Root of 76
√76 ≈ 8.717798
76 is not a perfect square, so √76 is an irrational number that is approximately 8.717798. In simplified radical form, √76 = 2√19.
√76 lies between √64 = 8 and √81 = 9.
| Number | 76 |
| Square root (decimal) | 8.717798 |
| Simplified radical | 2√19 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 76
76 = 2^2 × 19. This is what determines the simplified radical: for √76 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √76 = 2√19.
Estimating √76 by hand
√76 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 76 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.75 |
| Step 2 | 8.717857 |
| Step 3 | 8.717798 |
After 3 steps the estimate is 8.717798, matching √76 ≈ 8.717798.
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Frequently asked questions
Is 76 a perfect square?
No, 76 is not a perfect square, so its square root is irrational and approximately 8.717798.
What is the square root of 76 in simplest radical form?
√76 = 2√19 in simplest radical form.