√ 分母有理化计算器Rationalize the Denominator Calculator
把 a ÷ (b√c) 或 a ÷ (b + d√c) 形式的分数化为分母不含根号的最简形式：单项式分母乘以 √c，二项式分母乘以共轭式，并显示每一步。Rationalize fractions of the form a ÷ (b√c) or a ÷ (b + d√c): multiply by √c for a single-term denominator or by the conjugate for a two-term one, simplified, with every step shown.
使用说明与常见问题How-to & FAQ
「分母有理化计算器」是什么？What is the Rationalize the Denominator Calculator tool?
把 a ÷ (b√c) 或 a ÷ (b + d√c) 形式的分数化为分母不含根号的最简形式：单项式分母乘以 √c，二项式分母乘以共轭式，并显示每一步。Rationalize fractions of the form a ÷ (b√c) or a ÷ (b + d√c): multiply by √c for a single-term denominator or by the conjugate for a two-term one, simplified, with every step shown.
如何使用「分母有理化计算器」？How do I use the Rationalize the Denominator Calculator tool?
在「分母有理化计算器」中，填写「分母形式」、「分子 a」、「b」、「d（√c 的系数）」、「根号内 c」等参数，结果会随输入实时计算并显示在下方。In the Rationalize the Denominator Calculator: Fill in "Denominator form", "Numerator a", "b", "d (coefficient of √c)", "Radicand c"; results are recalculated instantly as you type.
为什么要分母有理化？Why rationalize the denominator?
分母不含根号的形式更便于比较大小、合并同类项和手算近似值，也是很多教材要求的最简形式。A root-free denominator makes values easier to compare, combine and estimate by hand, and many textbooks treat it as the simplest form.
共轭式是什么？What is the conjugate?
b + d√c 的共轭式是 b − d√c。两者相乘得 b² − d²c，根号消失，所以分子分母同乘共轭式就能有理化。The conjugate of b + d√c is b − d√c. Their product is b² − d²c, with no root, so multiplying top and bottom by the conjugate rationalizes the fraction.
计算精度如何？How precise are the results?
「分母有理化计算器」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The Rationalize the Denominator Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「分母有理化计算器」免费吗？需要注册吗？Is the Rationalize the Denominator Calculator free? Do I need an account?
「分母有理化计算器」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Rationalize the Denominator Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.