Square Root Calculator › Square root of 172
Square Root of 172
√172 ≈ 13.114877
172 is not a perfect square, so √172 is an irrational number that is approximately 13.114877. In simplified radical form, √172 = 2√43.
√172 lies between √169 = 13 and √196 = 14.
| Number | 172 |
| Square root (decimal) | 13.114877 |
| Simplified radical | 2√43 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 172
172 = 2^2 × 43. This is what determines the simplified radical: for √172 you pull out one copy of any prime that appears twice.
Here the paired factor 2 comes out from under the root, leaving √172 = 2√43.
Estimating √172 by hand
√172 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 172 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.115385 |
| Step 2 | 13.114877 |
| Step 3 | 13.114877 |
After 3 steps the estimate is 13.114877, matching √172 ≈ 13.114877.
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Frequently asked questions
Is 172 a perfect square?
No, 172 is not a perfect square, so its square root is irrational and approximately 13.114877.
What is the square root of 172 in simplest radical form?
√172 = 2√43 in simplest radical form.