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.