Square Root Calculator › Square root of 163
Square Root of 163
√163 ≈ 12.767145
163 is not a perfect square, so √163 is an irrational number that is approximately 12.767145. In simplified radical form, √163 = √163.
√163 lies between √144 = 12 and √169 = 13.
| Number | 163 |
| Square root (decimal) | 12.767145 |
| Simplified radical | √163 |
| Perfect square? | No |
| Rational? | No |
Calculate another square root
Prime factorization of 163
163 = 163. This is what determines the simplified radical: for √163 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √163 is already in simplest radical form as √163.
Estimating √163 by hand
√163 falls between √144 = 12 and √169 = 13, so it starts at 12.something. The Babylonian method refines that guess by averaging it with 163 ÷ the guess:
| Step | Estimate |
| Start | 12 |
| Step 1 | 12.791667 |
| Step 2 | 12.767169 |
| Step 3 | 12.767145 |
After 3 steps the estimate is 12.767145, matching √163 ≈ 12.767145.
Nearby square roots
Frequently asked questions
Is 163 a perfect square?
No, 163 is not a perfect square, so its square root is irrational and approximately 12.767145.
What is the square root of 163 in simplest radical form?
√163 = √163 in simplest radical form.