Square Root of 8
Calculate √8 instantly — exact value, step-by-step explanation, and properties.
How to Calculate √8
The square root of 8 is approximately 2.8284271247. Since 8 is not a perfect square, its square root is an irrational number. We know that √4 = 2 and √9 = 3, so √8 falls between 2 and 3. The simplified radical form is 2√2. To estimate manually: start with 2.8, then refine using the Babylonian method — guess a value, divide 8 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 8 by your guess: 8 ÷ 2.5 = 3.2000
- Average the result with your guess: (2.5 + 3.2000) ÷ 2 = 2.850000
- Repeat with the new estimate until you reach the desired precision.
√8 ≈ 2.8284271247 Properties of √8
Perfect Square?
No
8 is not a perfect square. Its root is irrational.
Decimal Value
2.8284271247
Rounded to 10 decimal places.
Simplified Form
2√2
Simplified by extracting perfect square factors from the radicand.
Square Root Symbol
√8
Also written as 8^(1/2) or 8^0.5 in programming.
Frequently Asked Questions
What is the square root of 8?
The square root of 8 is approximately 2.8284271247. This is an irrational number, which can be written in simplified radical form as 2√2.
Is 8 a perfect square?
No, 8 is not a perfect square. Its square root (2.8284271247...) is an irrational number that cannot be expressed as a simple fraction.
How do you calculate √8 by hand?
To calculate √8 by hand, use the Babylonian method: (1) Make an initial guess — since √4 = 2 and √9 = 3, start with 2.5. (2) Divide 8 by your guess. (3) Average the result with your guess. (4) Repeat steps 2-3 until you reach desired precision.
What is √8 in simplified radical form?
√8 can be simplified to 2√2. This is found by factoring out the largest perfect square from 8.