平方根计算器

找出数字的平方根及其简化的激进形式

平方根 —

简化激进 —

完美的广场? —

输入结果时更新。

这个计算器给你正确的答案了吗?

关于此计算器

A square root calculator gives the principal (positive) square root of a number, plus its simplified radical form and whether the number is a perfect square. Enter any non-negative number to see both the decimal value and the exact radical.

The simplified radical is found by pulling the largest perfect-square factor outside the root sign. For √72, the largest perfect square dividing 72 is 36, so √72 = √(36 × 2) = 6√2 — an exact form, unlike the rounded decimal 8.485. When the number is itself a perfect square, such as 36, the root is a whole number (6) and the tool flags it as a perfect square.

Square roots appear in the Pythagorean theorem, the distance formula, standard deviation and quadratic equations. Note that every positive number has two square roots, one positive and one negative; this tool returns the principal positive root, and negative inputs have no real square root.

经常问到的问题

什么是简化激进?

It rewrites a root by factoring out the largest perfect square. √72 = √(36×2) = 6√2, which is exact, unlike the rounded decimal 8.485.

数字的平方根总是正数吗?

每个正数数字有两个平方根,一个正方根,一个负方根。这个工具返回主(正)根,这是标准结果。

72的平方根是什么?

It is about 8.485, and its exact simplified form is 6√2.

什么是完美的广场?

整个数字的平方根也是整数,例如36(36=6),该工具可以说明数字是否合格。

我能拿负数的平方根吗?

实际数字中不是,负输入没有真正的平方根。你需要复杂的数字,其中4=2i。

为什么显示简化的激进而不是小数点?

The radical form is exact. 6√2 is precise, while 8.485 is a rounded approximation that loses accuracy in further calculations.

API - 使用代码中的计算器

将此计算器称为自由 JSON 端点。不需要按键。将字段值发送到下面作为查询参数或 JSON 。任何您省略的, 都会使用相同的默认值, 此页面预填的默认值是预填的; 未知参数是 400, 而不是静音零。读取 API 全部文件 →

终点

GET https://calculator.free/api/v1/square-root/

curl

curl "https://calculator.free/api/v1/square-root/?value=72"

JavaScript `fetch()`

const r = await fetch(
  "https://calculator.free/api/v1/square-root/?" + new URLSearchParams({
    "value": "72"
  }));
const data = await r.json();
console.log(data.results);

成果仅是一般指导的估计数,而不是财务、医疗或税务咨询。

关于此计算器

经常问到的问题

相关计算器

终点

curl

JavaScript fetch()

JavaScript `fetch()`