Square Root Calculator › Square root of 173
Square Root of 173
√173 ≈ 13.152946
173 is not a perfect square, so √173 is an irrational number that is approximately 13.152946. In simplified radical form, √173 = √173.
√173 lies between √169 = 13 and √196 = 14.
| Number | 173 |
| Square root (decimal) | 13.152946 |
| Simplified radical | √173 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 173
173 = 173. This is what determines the simplified radical: for √173 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √173 is already in simplest radical form as √173.
Estimating √173 by hand
√173 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 173 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.153846 |
| Step 2 | 13.152946 |
| Step 3 | 13.152946 |
After 3 steps the estimate is 13.152946, matching √173 ≈ 13.152946.
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Frequently asked questions
Is 173 a perfect square?
No, 173 is not a perfect square, so its square root is irrational and approximately 13.152946.
What is the square root of 173 in simplest radical form?
√173 = √173 in simplest radical form.