Square Root Calculator › Square root of 270
Square Root of 270
√270 ≈ 16.431677
270 is not a perfect square, so √270 is an irrational number that is approximately 16.431677. In simplified radical form, √270 = 3√30.
√270 lies between √256 = 16 and √289 = 17.
| Number | 270 |
| Square root (decimal) | 16.431677 |
| Simplified radical | 3√30 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 270
270 = 2 × 3^3 × 5. This is what determines the simplified radical: for √270 you pull out one copy of any prime that appears twice.
Here the paired factor 3 comes out from under the root, leaving √270 = 3√30.
Estimating √270 by hand
√270 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 270 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.4375 |
| Step 2 | 16.431678 |
| Step 3 | 16.431677 |
After 3 steps the estimate is 16.431677, matching √270 ≈ 16.431677.
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Frequently asked questions
Is 270 a perfect square?
No, 270 is not a perfect square, so its square root is irrational and approximately 16.431677.
What is the square root of 270 in simplest radical form?
√270 = 3√30 in simplest radical form.