Square Root of 2
Calculate √2 instantly — exact value, step-by-step explanation, and properties.
How to Calculate √2
The square root of 2 is approximately 1.4142135624. Since 2 is not a perfect square, its square root is an irrational number. We know that √1 = 1 and √4 = 2, so √2 falls between 1 and 2. To estimate manually: start with 1.4, then refine using the Babylonian method — guess a value, divide 2 by it, average the result with your guess, and repeat.
The Babylonian Method (Step by Step)
- Start with an initial guess. Since √1 = 1 and √4 = 2, a good starting guess is 1.5.
- Divide 2 by your guess: 2 ÷ 1.5 = 1.3333
- Average the result with your guess: (1.5 + 1.3333) ÷ 2 = 1.416667
- Repeat with the new estimate until you reach the desired precision.
√2 ≈ 1.4142135624 Properties of √2
Perfect Square?
No
2 is not a perfect square. Its root is irrational.
Decimal Value
1.4142135624
Rounded to 10 decimal places.
Square Root Symbol
√2
Also written as 2^(1/2) or 2^0.5 in programming.
Frequently Asked Questions
What is the square root of 2?
The square root of 2 is approximately 1.4142135624. This is an irrational number.
Is 2 a perfect square?
No, 2 is not a perfect square. Its square root (1.4142135624...) is an irrational number that cannot be expressed as a simple fraction.
How do you calculate √2 by hand?
To calculate √2 by hand, use the Babylonian method: (1) Make an initial guess — since √1 = 1 and √4 = 2, start with 1.5. (2) Divide 2 by your guess. (3) Average the result with your guess. (4) Repeat steps 2-3 until you reach desired precision.
What is √2 in simplified radical form?
√2 is already in its simplest radical form. The number 2 has no perfect square factors other than 1.