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.

Coefficient

Number under the root

Simplifies 1·√72. Leave the coefficient at 1 for a plain square root.

🔒 Calculated entirely in your browser — nothing is uploaded.

🔒 Nothing you enter is sent anywhere or stored. All processing happens in your browser.

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).

How it works — in four simple steps

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

Step 01

Enter the number

Type the number under the square root — the radicand.

Step 02

Add a coefficient (optional)

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

Step 03

Simplify

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

Step 04

Follow the steps

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

How it works

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

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.