Square Root Calculator › Square root of 160
Square Root of 160
√160 ≈ 12.649111
160 is not a perfect square, so √160 is an irrational number that is approximately 12.649111. In simplified radical form, √160 = 4√10.
√160 lies between √144 = 12 and √169 = 13.
| Number | 160 |
| Square root (decimal) | 12.649111 |
| Simplified radical | 4√10 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 160
160 = 2^5 × 5. This is what determines the simplified radical: for √160 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √160 = 4√10.
Estimating √160 by hand
√160 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 160 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.666667 |
| Step 2 | 12.649123 |
| Step 3 | 12.649111 |
After 3 steps the estimate is 12.649111, matching √160 ≈ 12.649111.
Nearby square roots
Frequently asked questions
Is 160 a perfect square?
No, 160 is not a perfect square, so its square root is irrational and approximately 12.649111.
What is the square root of 160 in simplest radical form?
√160 = 4√10 in simplest radical form.