Square Root Calculator › Square root of 280
Square Root of 280
√280 ≈ 16.733201
280 is not a perfect square, so √280 is an irrational number that is approximately 16.733201. In simplified radical form, √280 = 2√70.
√280 lies between √256 = 16 and √289 = 17.
| Number | 280 |
| Square root (decimal) | 16.733201 |
| Simplified radical | 2√70 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 280
280 = 2^3 × 5 × 7. This is what determines the simplified radical: for √280 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √280 = 2√70.
Estimating √280 by hand
√280 falls between √256 = 16 and √289 = 17, so it starts at 16.something. The Babylonian method refines that guess by averaging it with 280 ÷ the guess:
| Step | Estimate |
| Start | 16 |
| Step 1 | 16.75 |
| Step 2 | 16.733209 |
| Step 3 | 16.733201 |
After 3 steps the estimate is 16.733201, matching √280 ≈ 16.733201.
Nearby square roots
Frequently asked questions
Is 280 a perfect square?
No, 280 is not a perfect square, so its square root is irrational and approximately 16.733201.
What is the square root of 280 in simplest radical form?
√280 = 2√70 in simplest radical form.