Square Root Calculator › Square root of 80
Square Root of 80
√80 ≈ 8.944272
80 is not a perfect square, so √80 is an irrational number that is approximately 8.944272. In simplified radical form, √80 = 4√5.
√80 lies between √64 = 8 and √81 = 9.
| Number | 80 |
| Square root (decimal) | 8.944272 |
| Simplified radical | 4√5 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 80
80 = 2^4 × 5. This is what determines the simplified radical: for √80 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √80 = 4√5.
Estimating √80 by hand
√80 falls between √64 = 8 and √81 = 9, so it starts at 8.something. The Babylonian method refines that guess by averaging it with 80 ÷ the guess:
| Step | Estimate |
| Start | 8 |
| Step 1 | 9 |
| Step 2 | 8.944444 |
| Step 3 | 8.944272 |
After 3 steps the estimate is 8.944272, matching √80 ≈ 8.944272.
Nearby square roots
Frequently asked questions
Is 80 a perfect square?
No, 80 is not a perfect square, so its square root is irrational and approximately 8.944272.
What is the square root of 80 in simplest radical form?
√80 = 4√5 in simplest radical form.