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Square Root Calculator.

Find the square root of any number as a decimal and in simplified radical form, such as √72 = 6√2.

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Results update as you type.

Enter 0 or more. Whole numbers also get a simplified radical.

How to Use

The square root of a number is the value that multiplies by itself to give that number. 12 x 12 = 144, so the square root of 144 is 12.

Simplified radical form pulls the largest perfect-square factor out from under the radical sign: √72 = √(36 x 2) = 6√2. It is the exact answer, unlike a rounded decimal.

Negative numbers have no real square root, so this calculator asks for a number of 0 or more. Decimals are supported but are only shown as a decimal answer, not as a radical.

FAQs

How do you simplify a square root?

Find the largest perfect square that divides the number, then take its root outside the radical. For √72, the largest perfect-square factor is 36, so √72 = √(36 x 2) = 6√2. Simplified radical form is exact, unlike a rounded decimal such as 8.485.

What is a perfect square?

A perfect square is a number whose square root is a whole number, because it is some integer multiplied by itself: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 and so on. When you enter one, this calculator flags it and the radical disappears entirely — √144 is simply 12.

Why is √72 equal to 6√2?

72 factors as 36 x 2, and 36 is a perfect square. Since √(a x b) = √a x √b, you get √36 x √2 = 6√2. Stopping at 4 x 18 would give 2√18, which is correct but not fully simplified — always pull out the largest perfect square.

Can you take the square root of a negative number?

Not within the real numbers: any real number multiplied by itself is zero or positive, so nothing squares to a negative. Mathematicians define imaginary numbers for this (√-9 = 3i), but this calculator works in real numbers and asks for an input of 0 or more.

What is the square root of 0 and of 1?

Both are perfect squares and are their own square roots: √0 = 0 because 0 x 0 = 0, and √1 = 1 because 1 x 1 = 1. They are the only two numbers that equal their own square root.

Can I enter decimals?

Yes. The decimal square root is calculated for any non-negative number, so √2.25 = 1.5. Radical simplification is only shown for whole numbers, because pulling perfect-square factors out of a decimal has no standard simplified form.

Cite this calculator

Canonical URL: https://mathify.one/de/math/square-root

Cite as: Mathify. (2026). Quadratwurzelrechner. https://mathify.one/de/math/square-root

Use Cases

Simplifying radicals for math homework

Students can check their work when simplifying square roots, ensuring they have the correct simplified radical form and decimal approximation.

Example: Verify that √72 simplifies to 6√2 and equals approximately 8.485.

Quick reference for geometry and algebra

Teachers and professionals can quickly find exact square root values for calculations involving areas, distances, or quadratic equations.

Example: Find the side length of a square with area 50: √50 = 5√2 ≈ 7.071.

Frequently Asked Questions

What is simplified radical form?
Simplified radical form expresses a square root with no perfect square factors inside the radical. For example, √72 simplifies to 6√2 because 72 = 36 × 2, and √36 = 6. This form is often preferred in math for exactness.
How does the calculator detect perfect squares?
The calculator checks if the input number is a perfect square (like 16, 25, 100). If it is, the square root is an integer, and the result is shown as that integer without a radical. For non-perfect squares, it simplifies the radical by factoring out perfect square factors.
Can I use this calculator for negative numbers?
No, the square root of a negative number is not a real number. This calculator is designed for non-negative numbers only. For negative inputs, you would need to use complex numbers, which are not supported here.

Tips & Common Mistakes

Tips

  • Enter a positive number to get both the decimal and simplified radical form. For perfect squares, the radical form is just the integer.
  • Use the simplified radical form when you need an exact answer, and the decimal form when you need a practical approximation.
  • If you're solving equations, keep the radical form to avoid rounding errors in further calculations.
  • Check if your number has factors that are perfect squares (like 4, 9, 16) to manually verify the simplification.

Common Mistakes to Avoid

  • Forgetting to simplify the radical completely, e.g., leaving √72 as 2√18 instead of 6√2.
  • Assuming the decimal form is exact; it's an approximation, so use the radical form for precise math.
  • Entering negative numbers expecting a real result; square roots of negatives are not real numbers.

Last updated: August 13, 2026