Square Root of 6
Calculate √6 instantly — exact value, step-by-step explanation, and properties.
How to Calculate √6
The square root of 6 is approximately 2.4494897428. Since 6 is not a perfect square, its square root is an irrational number. We know that √4 = 2 and √9 = 3, so √6 falls between 2 and 3. To estimate manually: start with 2.4, then refine using the Babylonian method — guess a value, divide 6 by it, average the result with your guess, and repeat.
The Babylonian Method (Step by Step)
- Start with an initial guess. Since √4 = 2 and √9 = 3, a good starting guess is 2.5.
- Divide 6 by your guess: 6 ÷ 2.5 = 2.4000
- Average the result with your guess: (2.5 + 2.4000) ÷ 2 = 2.450000
- Repeat with the new estimate until you reach the desired precision.
√6 ≈ 2.4494897428 Properties of √6
Perfect Square?
No
6 is not a perfect square. Its root is irrational.
Decimal Value
2.4494897428
Rounded to 10 decimal places.
Square Root Symbol
√6
Also written as 6^(1/2) or 6^0.5 in programming.
Frequently Asked Questions
What is the square root of 6?
The square root of 6 is approximately 2.4494897428. This is an irrational number.
Is 6 a perfect square?
No, 6 is not a perfect square. Its square root (2.4494897428...) is an irrational number that cannot be expressed as a simple fraction.
How do you calculate √6 by hand?
To calculate √6 by hand, use the Babylonian method: (1) Make an initial guess — since √4 = 2 and √9 = 3, start with 2.5. (2) Divide 6 by your guess. (3) Average the result with your guess. (4) Repeat steps 2-3 until you reach desired precision.
What is √6 in simplified radical form?
√6 is already in its simplest radical form. The number 6 has no perfect square factors other than 1.