Square Root Calculator › Square root of 170
Square Root of 170
√170 ≈ 13.038405
170 is not a perfect square, so √170 is an irrational number that is approximately 13.038405. In simplified radical form, √170 = √170.
√170 lies between √169 = 13 and √196 = 14.
| Number | 170 |
| Square root (decimal) | 13.038405 |
| Simplified radical | √170 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 170
170 = 2 × 5 × 17. This is what determines the simplified radical: for √170 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √170 is already in simplest radical form as √170.
Estimating √170 by hand
√170 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 170 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 13.038462 |
| Step 2 | 13.038405 |
| Step 3 | 13.038405 |
After 3 steps the estimate is 13.038405, matching √170 ≈ 13.038405.
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Frequently asked questions
Is 170 a perfect square?
No, 170 is not a perfect square, so its square root is irrational and approximately 13.038405.
What is the square root of 170 in simplest radical form?
√170 = √170 in simplest radical form.