Square Root Calculator › Square root of 72
Square Root of 72
√72 ≈ 8.485281
72 is not a perfect square, so √72 is an irrational number that is approximately 8.485281. In simplified radical form, √72 = 6√2.
√72 lies between √64 = 8 and √81 = 9.
| Number | 72 |
| Square root (decimal) | 8.485281 |
| Simplified radical | 6√2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 72
72 = 2^3 × 3^2. This is what determines the simplified radical: for √72 you pull out one copy of any prime that appears twice.
Here the paired factors 2 and 3 come out from under the root, leaving √72 = 6√2.
Estimating √72 by hand
√72 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 72 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 8.5 |
| Step 2 | 8.485294 |
| Step 3 | 8.485281 |
After 3 steps the estimate is 8.485281, matching √72 ≈ 8.485281.
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Frequently asked questions
Is 72 a perfect square?
No, 72 is not a perfect square, so its square root is irrational and approximately 8.485281.
What is the square root of 72 in simplest radical form?
√72 = 6√2 in simplest radical form.