Square Root Calculator › Square root of 96
Square Root of 96
√96 ≈ 9.797959
96 is not a perfect square, so √96 is an irrational number that is approximately 9.797959. In simplified radical form, √96 = 4√6.
√96 lies between √81 = 9 and √100 = 10.
| Number | 96 |
| Square root (decimal) | 9.797959 |
| Simplified radical | 4√6 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 96
96 = 2^5 × 3. This is what determines the simplified radical: for √96 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √96 = 4√6.
Estimating √96 by hand
√96 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 96 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.833333 |
| Step 2 | 9.798023 |
| Step 3 | 9.797959 |
After 3 steps the estimate is 9.797959, matching √96 ≈ 9.797959.
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Frequently asked questions
Is 96 a perfect square?
No, 96 is not a perfect square, so its square root is irrational and approximately 9.797959.
What is the square root of 96 in simplest radical form?
√96 = 4√6 in simplest radical form.