Square Root Calculator

1. Enter any positive number. For square roots of negative numbers, the result is imaginary (not calculated here). Decimals and large numbers are fully supported.
2. Select the root type. Square root (2nd root, n=2) is the default. Cube root (n=3) finds what number cubed equals the input. Change n to any value for any nth root.
3. Read the results. The calculator shows the decimal result, the simplified radical form (e.g., √50 = 5√2), and the step-by-step factorization. The inverse (squaring the result) is also shown to verify accuracy.

Square root:     √x = x^(1/2)
Cube root:       ∛x = x^(1/3)
Nth root:        ⁿ√x = x^(1/n)

Product rule:    √(a × b) = √a × √b
Quotient rule:   √(a/b) = √a / √b
Power rule:      √(aⁿ) = a^(n/2)

Simplifying:     √72 = √(36 × 2) = 6√2
√200 = √(100 × 2) = 10√2
√48 = √(16 × 3) = 4√3

Perfect squares (their square roots are whole numbers):