Square Root Calculator
How It Works
This square root calculator uses established formulas to provide accurate results.
The basic rule:
- √(a × b) = √a × √b
- √(a²) = |a|
- Simplify: find largest perfect square factor
Results are estimates. Consult a professional for critical decisions.
Frequently Asked Questions
What is a square root?
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, √25 = 5 because 5 × 5 = 25.
What is a perfect square?
A perfect square is a number that has a whole number as its square root. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100. These are the squares of 1, 2, 3, 4, 5, 6, 7, 8, 9, 10.
How do you simplify a square root?
Factor out the largest perfect square. For example, √72 = √(36 × 2) = √36 × √2 = 6√2. Look for perfect square factors like 4, 9, 16, 25, 36, etc.
Can you take the square root of a negative number?
Not with real numbers. The square root of a negative number involves imaginary numbers (using i, where i = √(-1)). In middle school math, square roots of negative numbers are considered undefined.