🔢 Math Calculator

📐 How It Works

Finds the number which, when multiplied by itself, equals the given value. Every positive number has two square roots: positive and negative.

🔢 Worked Examples

• √144 = 12
• √2 ≈ 1.41421 (irrational)
• √225 = 15
• √0.25 = 0.5
• √-1 = i (complex number)

📋 Common Use Cases

• Pythagorean theorem — finding a hypotenuse
• Physics — velocity from kinetic energy (v = √(2KE/m))
• Statistics — standard deviation involves √(variance)
• Electrical engineering — RMS voltage = peak ÷ √2

💡 Did You Know?

The ancient Babylonians had a method for computing square roots accurate to 6 decimal places around 1700 BCE. The "Babylonian method" (iterative: xₙ₊₁ = ½(xₙ + S/xₙ)) is still used today in computing.

⚠️ Common Mistake

√(a+b) ≠ √a + √b. For example √(9+16) = √25 = 5, but √9 + √16 = 3 + 4 = 7.