Square Root Calculator › Square root of 2
Square Root of 2
√2 ≈ 1.414214
2 is not a perfect square, so √2 is an irrational number that is approximately 1.414214. In simplified radical form, √2 = √2.
√2 lies between √1 = 1 and √4 = 2.
| Number | 2 |
| Square root (decimal) | 1.414214 |
| Simplified radical | √2 |
| Perfect square? | No |
| Rational? | No |
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Prime factorization of 2
2 = 2. This is what determines the simplified radical: for √2 you pull out one copy of any prime that appears twice.
No prime appears twice, so nothing can be taken out — √2 is already in simplest radical form as √2.
Estimating √2 by hand
√2 falls between √1 = 1 and √4 = 2, so it starts at 1.something. The Babylonian method refines that guess by averaging it with 2 ÷ the guess:
| Step | Estimate |
| Start | 1 |
| Step 1 | 1.5 |
| Step 2 | 1.416667 |
| Step 3 | 1.414216 |
After 3 steps the estimate is 1.414216, matching √2 ≈ 1.414214.
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Frequently asked questions
Is 2 a perfect square?
No, 2 is not a perfect square, so its square root is irrational and approximately 1.414214.
What is the square root of 2 in simplest radical form?
√2 = √2 in simplest radical form.