Square Root Calculator › Square root of 79
Square Root of 79
√79 ≈ 8.888194
79 is not a perfect square, so √79 is an irrational number that is approximately 8.888194. In simplified radical form, √79 = √79.
√79 lies between √64 = 8 and √81 = 9.
| Number | 79 |
| Square root (decimal) | 8.888194 |
| Simplified radical | √79 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 79
79 = 79. This is what determines the simplified radical: for √79 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √79 is already in simplest radical form as √79.
Estimating √79 by hand
√79 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 79 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.9375 |
| Step 2 | 8.88833 |
| Step 3 | 8.888194 |
After 3 steps the estimate is 8.888194, matching √79 ≈ 8.888194.
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Frequently asked questions
Is 79 a perfect square?
No, 79 is not a perfect square, so its square root is irrational and approximately 8.888194.
What is the square root of 79 in simplest radical form?
√79 = √79 in simplest radical form.