Square Root Calculator

Calculate square roots, cube roots, and nth roots.

Common Perfect Squares
√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√121 = 11
√144 = 12
√169 = 13
√196 = 14
√225 = 15

Frequently Asked Questions

How does the square root calculator work?

The calculator computes the principal (positive) square root of your number. For example, sqrt(144) = 12, sqrt(2) = 1.41421... It shows both the exact decimal value and the simplified radical form when applicable. For perfect squares (4, 9, 16, 25...), the result is a whole number.

Can I calculate cube roots and other roots?

Yes — enter the root degree (2 for square root, 3 for cube root, 4 for fourth root, etc.) and the number. Cube root of 27 = 3, fourth root of 81 = 3, fifth root of 32 = 2. Non-integer roots are displayed as decimals with configurable precision.

What is a simplified radical form?

Simplified radical form extracts perfect square factors. For example, sqrt(72) = sqrt(36 x 2) = 6*sqrt(2). The calculator finds the largest perfect square factor and simplifies automatically. This form is preferred in mathematics over long decimal approximations.

Can I find the square root of negative numbers?

The square root of a negative number produces an imaginary result. sqrt(-9) = 3i, where i is the imaginary unit (sqrt(-1)). The calculator handles negative inputs and displays the complex number result. Odd roots of negative numbers are real: cube root of -8 = -2.

What are some common perfect squares I should know?

Key perfect squares: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400. Knowing these helps with mental math and simplifying radicals. The calculator instantly identifies whether your input is a perfect square.