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Simplify Square Root Calculator

Reduce a square root to its simplest radical form — like √72 = 6√2 — with the factoring steps shown and the decimal value alongside.

Quick presets

Simplify Square Root Calculator

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Prime factors
Simplest radical form
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Steps
    Perfect powers to look for

    Runs in your browser — nothing you enter is uploaded or stored.

    ToolFeather · Radical form
    Scratchpad auto-saved
    Stored in this browser (localStorage)
    Step-by-step~40s read

    How it works — in four simple steps

    No signup and nothing to install — it all runs in your browser.

    1

    Enter the number

    Type the number under the square root — the radicand.

    2

    Add a coefficient (optional)

    Leave it at 1 for a plain root, or set it to simplify things like 3√50.

    3

    Simplify

    Press Simplify to get the simplest radical form and the decimal value.

    4

    Follow the steps

    Read the factoring steps to see exactly how the perfect square was pulled out.

    Pro tip

    Pull out the largest perfect-square factor: √72 = √(36 × 2) = 6√2.

    Features

    Simplest radical form

    Reduces any square root to a·√b with the smallest possible number left under the root — the answer maths teachers expect.

    Step-by-step factoring

    Shows the largest perfect-square factor, the split, and the final simplification, so it teaches the method rather than hiding it.

    Decimal value too

    Gives the exact radical form and the decimal approximation side by side, so you can use whichever the question wants.

    Coefficients & negatives

    Simplify expressions like 3√50, and negative radicands return a clean imaginary result (× i).

    About the Simplify Square Root Calculator

    Simplifying a square root means pulling out the largest perfect-square factor from under the radical, so the number left inside is as small as possible. For example √72 isn't in simplest form because 72 = 36 × 2, and 36 is a perfect square — so √72 = √36 · √2 = 6√2.

    This calculator finds the largest perfect square that divides your number, takes its root out front, and leaves the rest inside the radical. It shows the simplest radical form, the decimal value, and the step-by-step factoring so you can follow the method. An optional coefficient lets you simplify things like 3√50 = 15√2, and negative numbers return an imaginary result (× i).

    It's all done in your browser with exact integer factoring — nothing is uploaded, and it works offline.

    Examples

    √72 = 6√2  (72 = 36 × 2)
    √50 = 5√2  ·  3√50 = 15√2
    √13 stays √13 (prime — already simplest)  ·  √64 = 8

    Frequently asked questions

    5 answers
    How do you simplify a square root?
    Find the largest perfect-square factor of the number, take its square root outside the radical, and leave the rest inside. For √72: 72 = 36 × 2, so √72 = 6√2. This tool does the factoring and shows each step.
    What is the simplest radical form?
    It's the form a√b where b has no perfect-square factors left. √72 in simplest radical form is 6√2. If the number is prime or square-free, the root is already in simplest form.
    Can it simplify with a coefficient, like 3√50?
    Yes — enter the coefficient and the radicand, and it multiplies through: 3√50 = 3 × 5√2 = 15√2.
    What about the square root of a negative number?
    Negative radicands have no real square root, so the tool returns an imaginary result, e.g. √−8 = 2√2 i, where i is the imaginary unit.
    Does it also give a decimal?
    Yes. Alongside the exact radical form it shows the decimal approximation, so you can use whichever your problem requires.