Square Root Calculator › Square root of 68
Square Root of 68
√68 ≈ 8.246211
68 is not a perfect square, so √68 is an irrational number that is approximately 8.246211. In simplified radical form, √68 = 2√17.
√68 lies between √64 = 8 and √81 = 9.
| Number | 68 |
| Square root (decimal) | 8.246211 |
| Simplified radical | 2√17 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 68
68 = 2^2 × 17. This is what determines the simplified radical: for √68 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √68 = 2√17.
Estimating √68 by hand
√68 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 68 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.25 |
| Step 2 | 8.246212 |
| Step 3 | 8.246211 |
After 3 steps the estimate is 8.246211, matching √68 ≈ 8.246211.
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Frequently asked questions
Is 68 a perfect square?
No, 68 is not a perfect square, so its square root is irrational and approximately 8.246211.
What is the square root of 68 in simplest radical form?
√68 = 2√17 in simplest radical form.