Square Root Calculator
Calculate square roots
Frequently Asked Questions
How does the Square Root Calculator work?
Enter any non-negative number to find its square root. √144 = 12, √2 ≈ 1.41421. The calculator provides results to 10 decimal places and also shows whether the result is a perfect square (integer result).
What is a perfect square?
A perfect square is a number whose square root is an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144. The calculator identifies perfect squares and shows the simplified radical form for non-perfect squares.
How do I simplify a square root?
Factor out perfect squares: √72 = √(36 × 2) = 6√2. √200 = √(100 × 2) = 10√2. The calculator shows both the decimal approximation and the simplified radical form.
Can I calculate the square root of a negative number?
The square root of a negative number involves imaginary numbers: √(-9) = 3i, where i = √(-1). The calculator handles complex results and displays them in a+bi form when the input is negative.
What is the relationship between square roots and exponents?
√x = x^(1/2). The nth root is x^(1/n). So ³√8 = 8^(1/3) = 2. This relationship extends to any fractional exponent: x^(m/n) = ⁿ√(x^m). The calculator supports any root, not just square roots.