Square Root Calculator › Square root of 195
Square Root of 195
√195 ≈ 13.96424
195 is not a perfect square, so √195 is an irrational number that is approximately 13.96424. In simplified radical form, √195 = √195.
√195 lies between √169 = 13 and √196 = 14.
| Number | 195 |
| Square root (decimal) | 13.96424 |
| Simplified radical | √195 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 195
195 = 3 × 5 × 13. This is what determines the simplified radical: for √195 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √195 is already in simplest radical form as √195.
Estimating √195 by hand
√195 falls between √169 = 13 and √196 = 14, so it starts at 13.something. The Babylonian method refines that guess by averaging it with 195 ÷ the guess:
| Step | Estimate |
| Start | 13 |
| Step 1 | 14 |
| Step 2 | 13.964286 |
| Step 3 | 13.96424 |
After 3 steps the estimate is 13.96424, matching √195 ≈ 13.96424.
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Frequently asked questions
Is 195 a perfect square?
No, 195 is not a perfect square, so its square root is irrational and approximately 13.96424.
What is the square root of 195 in simplest radical form?
√195 = √195 in simplest radical form.