Square Root of 15
Calculate √15 instantly — exact value, step-by-step explanation, and properties.
How to Calculate √15
The square root of 15 is approximately 3.8729833462. Since 15 is not a perfect square, its square root is an irrational number. We know that √9 = 3 and √16 = 4, so √15 falls between 3 and 4. To estimate manually: start with 3.8, then refine using the Babylonian method — guess a value, divide 15 by it, average the result with your guess, and repeat.
The Babylonian Method (Step by Step)
- Start with an initial guess. Since √9 = 3 and √16 = 4, a good starting guess is 3.5.
- Divide 15 by your guess: 15 ÷ 3.5 = 4.2857
- Average the result with your guess: (3.5 + 4.2857) ÷ 2 = 3.892857
- Repeat with the new estimate until you reach the desired precision.
√15 ≈ 3.8729833462 Properties of √15
Perfect Square?
No
15 is not a perfect square. Its root is irrational.
Decimal Value
3.8729833462
Rounded to 10 decimal places.
Square Root Symbol
√15
Also written as 15^(1/2) or 15^0.5 in programming.
Related Square Root Values
Reference table of square roots near 15 for quick comparison.
Frequently Asked Questions
What is the square root of 15?
The square root of 15 is approximately 3.8729833462. This is an irrational number.
Is 15 a perfect square?
No, 15 is not a perfect square. Its square root (3.8729833462...) is an irrational number that cannot be expressed as a simple fraction.
How do you calculate √15 by hand?
To calculate √15 by hand, use the Babylonian method: (1) Make an initial guess — since √9 = 3 and √16 = 4, start with 3.5. (2) Divide 15 by your guess. (3) Average the result with your guess. (4) Repeat steps 2-3 until you reach desired precision.
What is √15 in simplified radical form?
√15 is already in its simplest radical form. The number 15 has no perfect square factors other than 1.