Square Root Calculator › Square root of 205
Square Root of 205
√205 ≈ 14.317821
205 is not a perfect square, so √205 is an irrational number that is approximately 14.317821. In simplified radical form, √205 = √205.
√205 lies between √196 = 14 and √225 = 15.
| Number | 205 |
| Square root (decimal) | 14.317821 |
| Simplified radical | √205 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 205
205 = 5 × 41. This is what determines the simplified radical: for √205 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √205 is already in simplest radical form as √205.
Estimating √205 by hand
√205 falls between √196 = 14 and √225 = 15, so it starts at 14.something. The Babylonian method refines that guess by averaging it with 205 ÷ the guess:
| Step | Estimate |
| Start | 14 |
| Step 1 | 14.321429 |
| Step 2 | 14.317822 |
| Step 3 | 14.317821 |
After 3 steps the estimate is 14.317821, matching √205 ≈ 14.317821.
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Frequently asked questions
Is 205 a perfect square?
No, 205 is not a perfect square, so its square root is irrational and approximately 14.317821.
What is the square root of 205 in simplest radical form?
√205 = √205 in simplest radical form.