Square Root Calculator › Square root of 175
Square Root of 175
√175 ≈ 13.228757
175 is not a perfect square, so √175 is an irrational number that is approximately 13.228757. In simplified radical form, √175 = 5√7.
√175 lies between √169 = 13 and √196 = 14.
| Number | 175 |
| Square root (decimal) | 13.228757 |
| Simplified radical | 5√7 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 175
175 = 5^2 × 7. This is what determines the simplified radical: for √175 you pull out one copy of any prime that appears twice.
Here the paired factor 5 comes out from under the root, leaving √175 = 5√7.
Estimating √175 by hand
√175 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 175 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.230769 |
| Step 2 | 13.228757 |
| Step 3 | 13.228757 |
After 3 steps the estimate is 13.228757, matching √175 ≈ 13.228757.
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Frequently asked questions
Is 175 a perfect square?
No, 175 is not a perfect square, so its square root is irrational and approximately 13.228757.
What is the square root of 175 in simplest radical form?
√175 = 5√7 in simplest radical form.