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 surd form. It finds the largest perfect square factor of the number under the square root and rewrites the expression in simplified radical form instantly.
Simply type a positive number inside the input field. The calculator works for whole numbers such as:
Results update automatically as you type.
The calculator:
This guarantees the result is always shown in fully simplified surd form.
The calculator ensures safe and accurate results:
Clear error messages guide users when input is incorrect.
Results appear instantly without reloading the page.
1. You enter a positive number n under the square root.
2. The calculator searches for the largest perfect square factor of n.
3. It separates n into:
n = (perfect square) × (remaining factor)
4. The square root of the perfect square moves outside √.
5. The remaining factor stays inside √.
6. The simplified surd form is displayed instantly.
All calculations are performed using JavaScript in real time, 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 (√ numbers) into their exact surd form. It extracts the largest perfect square factor and rewrites the radical in simplified form.
It searches for the largest perfect square that divides the number. That square root is moved outside the radical sign, and the remaining factor stays inside √.
Yes. If the number under the radical is a perfect square (such as 16, 25, or 144), the calculator will return a whole number instead of a radical.
No. This calculator only works with positive real numbers. Negative inputs are not supported because their square roots are imaginary numbers.
The calculator is designed primarily for whole numbers. Decimal inputs may not simplify correctly if they do not form exact perfect square factors.
The calculator displays an error message because the tool is restricted to positive numbers greater than zero.
Yes. The calculator displays results in exact simplified radical (surd) form rather than decimal approximations.
Yes, it is completely free to use with no registration required.
Yes. The Surd Simplifier is fully responsive and works on smartphones, tablets, laptops, and desktop devices.
Students, teachers, and anyone studying algebra or preparing for exams can use this tool to simplify radicals quickly and verify their answers.
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