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.

数学

即时、私密且免费

平方根计算器.

以小数形式和简化根式形式（如√72 = 6√2）求任意数字的平方根。

此计算器尚未完全翻译——部分文本以英文显示。

设备端计算无需注册

输入数值

输入时结果会更新。

02 / 答案

数字请输入0或更大的数。整数还会给出化简后的根式。

请输入0或更大的数。整数还会给出化简后的根式。

使用方法

一个数的平方根是与自身相乘后等于该数的值。12 × 12 = 144，因此144的平方根是12。

化简根式的做法是将根号下最大的完全平方因数提取出来：√72 = √(36 × 2) = 6√2。这是精确答案，不同于四舍五入的小数。

负数没有实数平方根，因此本计算器要求输入0或更大的数。支持小数输入，但仅以小数形式给出答案，不显示根式。

Cite this calculator

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

Cite as: Mathify. (n.d.). 平方根计算器. https://mathify.one/zh/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