Simplify square roots and radical expressions instantly. Enter a number and get its simplified surd form.
This calculator simplifies square roots (radicals) into their exact simplified surd form. It automatically finds the largest perfect square factor of the number under √ and rewrites the radical expression in simplest form instantly.
Simply type a positive number under the square root symbol. For example:
The result updates automatically as you type.
The calculator:
This guarantees the radical is shown in fully simplified form.
The calculator ensures safe and correct results:
Clear error messages guide the user when input is incorrect.
Results appear instantly without page reload:
1. Enter a positive number n under the square root.
2. The calculator finds the largest perfect square factor of n.
3. It rewrites n as:
n = (perfect square) × (remaining factor)
4. The square root of the perfect square moves outside √.
5. The remaining factor stays inside √.
6. The simplified radical form is displayed instantly.
All calculations are performed in real time using JavaScript, ensuring fast and accurate radical simplification.
Suppose you enter:
√72
The calculator finds:
72 = 36 × 2
√72 = √(36 × 2)
√72 = 6√2
The largest perfect square factor (36) is extracted, leaving 2 inside the radical.
Everything you need to know about simplifying square roots and radical expressions accurately and instantly.
This calculator simplifies square roots by extracting the largest perfect square factor from the number under the radical symbol (√). It rewrites the expression in fully simplified surd form instantly.
A surd (also called a radical) is a square root that cannot be simplified into a whole number. For example, √2 and √5 are surds, while √144 equals 12 because it is a perfect square.
You can enter any positive real number under the square root. The calculator does not allow zero or negative values because the current version works only with real square roots.
Yes. If you enter a perfect square such as 16, 36, or 144, the calculator will return a whole number (for example, √144 = 12).
It finds the largest perfect square factor of the number, separates it into (perfect square × remaining factor), moves the square root of the perfect square outside the radical, and leaves the remaining factor inside √.
If you enter zero, a negative number, or an empty value, the calculator displays an error message asking you to enter a valid positive number.
Yes, the calculator is completely free to use online. No registration, download, or payment is required.
Yes. The calculator is fully responsive and works smoothly on smartphones, tablets, laptops, and desktop computers.
No. This version is designed specifically for square roots (√). It does not currently support cube roots or higher-order radicals.
Students learning algebra, teachers explaining radical simplification, and anyone checking homework or practicing square root problems can use this tool for fast and accurate results.
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