Square Root Calculator › Square root of 3
Square Root of 3
√3 ≈ 1.732051
3 is not a perfect square, so √3 is an irrational number that is approximately 1.732051. In simplified radical form, √3 = √3.
√3 lies between √1 = 1 and √4 = 2.
| Number | 3 |
| Square root (decimal) | 1.732051 |
| Simplified radical | √3 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 3
3 = 3. This is what determines the simplified radical: for √3 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √3 is already in simplest radical form as √3.
Estimating √3 by hand
√3 falls between √1 = 1 and √4 = 2, so it starts at 1.something. The Babylonian method refines that guess by averaging it with 3 ÷ the guess:
| Step | Estimate |
| Start | 1 |
| Step 1 | 2 |
| Step 2 | 1.75 |
| Step 3 | 1.732143 |
After 3 steps the estimate is 1.732143, matching √3 ≈ 1.732051.
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Frequently asked questions
Is 3 a perfect square?
No, 3 is not a perfect square, so its square root is irrational and approximately 1.732051.
What is the square root of 3 in simplest radical form?
√3 = √3 in simplest radical form.