Square Root Calculator

Find square roots, cube roots and any nth root.

Square root of 72

8.48528137

Simplified: 6√2

Simplified radical

6√2

Squared back

72.00000000

Perfect power

Rounded

8.49

√72 = 8.48528137

√72 simplifies by pulling out the largest perfect square factor.

What does Square Root Calculator do?

Calculate square, cube and nth roots to high precision, with perfect squares identified and results given in simplified radical form where possible — which is what algebra homework usually asks for.

How to Use Square Root Calculator

1
Enter a numberPositive or negative.
2
Choose the rootSquare, cube, or type any n.
3
Read the resultDecimal and simplified radical form.

Key Features

Square, cube and any nth root
Perfect squares and cubes identified exactly
Simplified radical form, such as √72 = 6√2
Adjustable decimal precision up to 15 significant digits
Negative inputs handled, with imaginary results labelled
Prime factorisation shown to explain the simplification

Frequently Asked Questions

How do I simplify a square root?

Factor out the largest perfect square. √72 = √(36 × 2) = 6√2. The calculator does this by prime factorisation and shows the working.

What is the square root of a negative number?

Not a real number. √−9 is 3i, where i is the imaginary unit. The calculator reports it in that form rather than returning an error.

What is a perfect square?

A number whose square root is a whole number: 1, 4, 9, 16, 25 and so on. The tool tells you when your input is one, and gives the exact root.

How do I calculate a cube root by hand?

Estimate and refine. To find ∛343, note 7³ = 343, so the answer is 7. For non-perfect cubes, Newton’s method converges quickly — the calculator uses a high-precision equivalent.

Runs in your browser

All arithmetic runs in your browser, using exact BigInt maths where whole numbers are involved so nothing is lost to floating-point rounding.

How the rest of the site handles data