Square Root Calculator › Square root of 90
Square Root of 90
√90 ≈ 9.486833
90 is not a perfect square, so √90 is an irrational number that is approximately 9.486833. In simplified radical form, √90 = 3√10.
√90 lies between √81 = 9 and √100 = 10.
| Number | 90 |
| Square root (decimal) | 9.486833 |
| Simplified radical | 3√10 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 90
90 = 2 × 3^2 × 5. This is what determines the simplified radical: for √90 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √90 = 3√10.
Estimating √90 by hand
√90 falls between √81 = 9 and √100 = 10, so it starts at 9.something. The Babylonian method refines that guess by averaging it with 90 ÷ the guess:
| Step | Estimate |
| Start | 9 |
| Step 1 | 9.5 |
| Step 2 | 9.486842 |
| Step 3 | 9.486833 |
After 3 steps the estimate is 9.486833, matching √90 ≈ 9.486833.
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Frequently asked questions
Is 90 a perfect square?
No, 90 is not a perfect square, so its square root is irrational and approximately 9.486833.
What is the square root of 90 in simplest radical form?
√90 = 3√10 in simplest radical form.