Square Root of 200
Calculate √200 instantly — exact value, step-by-step explanation, and properties.
How to Calculate √200
The square root of 200 is approximately 14.1421356237. Since 200 is not a perfect square, its square root is an irrational number. We know that √196 = 14 and √225 = 15, so √200 falls between 14 and 15. The simplified radical form is 10√2. To estimate manually: start with 14.1, then refine using the Babylonian method — guess a value, divide 200 by it, average the result with your guess, and repeat.
The Babylonian Method (Step by Step)
- Start with an initial guess. Since √196 = 14 and √225 = 15, a good starting guess is 14.5.
- Divide 200 by your guess: 200 ÷ 14.5 = 13.7931
- Average the result with your guess: (14.5 + 13.7931) ÷ 2 = 14.146552
- Repeat with the new estimate until you reach the desired precision.
√200 ≈ 14.1421356237 Properties of √200
Perfect Square?
No
200 is not a perfect square. Its root is irrational.
Decimal Value
14.1421356237
Rounded to 10 decimal places.
Simplified Form
10√2
Simplified by extracting perfect square factors from the radicand.
Square Root Symbol
√200
Also written as 200^(1/2) or 200^0.5 in programming.
Frequently Asked Questions
What is the square root of 200?
The square root of 200 is approximately 14.1421356237. This is an irrational number, which can be written in simplified radical form as 10√2.
Is 200 a perfect square?
No, 200 is not a perfect square. Its square root (14.1421356237...) is an irrational number that cannot be expressed as a simple fraction.
How do you calculate √200 by hand?
To calculate √200 by hand, use the Babylonian method: (1) Make an initial guess — since √196 = 14 and √225 = 15, start with 14.5. (2) Divide 200 by your guess. (3) Average the result with your guess. (4) Repeat steps 2-3 until you reach desired precision.
What is √200 in simplified radical form?
√200 can be simplified to 10√2. This is found by factoring out the largest perfect square from 200.