无理数平方根计算
At times, in everyday situations, we may face the task of having to figure the square root of a number. What if there is no calculator or a smartphone handy? Can we use an old fashioned paper and pencil to do it in a long division style?
有时，在日常情况下，我们可能面临必须计算数字平方根的任务。 如果没有便携式计算器或智能手机怎么办？ 我们可以用老式的纸和铅笔做长分区样式吗？
Yes we can, and there are several different methods. Some are more complex than others. Some provide more accurate results.
是的，我们可以，并且有几种不同的方法。 有些比其他复杂。 一些提供更准确的结果。
The one I want to share with you is one of them. To make this article more reader friendly, each step comes with illustrations.
我想与您分享的就是其中之一。 为了使本文对读者更友好，每个步骤都附带插图。
步骤1：将数字成对分开 (STEP 1: Separate The Digits Into Pairs )
To begin, let’s organize the workspace. We will divide the space into three parts. Then, let’s separate the number’s digits into pairs moving from right to left.
首先，让我们组织工作区。 我们将空间分为三个部分。 然后，我们将数字分开成对，从右向左移动。
For example, the number 7,469.17 becomes 74 69. 17. Or in the case of a number with an odd amount of digits such as 19,036, we will start with 1 90 36.
例如，数字7,469.17变为74 69. 17 。 或者，对于一个数字为奇数的数字，例如19,036，我们将从1 90 36开始。
In our case here, 2,025 becomes 20 25.
在我们这里的例子中，2,025变为20 25 。
步骤2：找出最大的整数 (STEP 2: Find The Largest Integer)
As the next step, we need to find the largest integer (i) whose square is less than or equal to the leftmost number.
下一步，我们需要找到平方小于或等于最左数的最大整数(i)。
In our current example the leftmost number is 20. Since 4² = 16 <= 20 and 5² = 25 > 20, the integer in question is 4. Let’s deposit 4 to the top-right corner and 4² = 16 to the bottom right one.
在我们当前的示例中，最左边的数字是20。由于4²= 16 <= 20和5²= 25> 20，所讨论的整数是4。让我们将4存入右上角，将4²= 16存入右下角。
步骤3：现在减去该整数 (STEP 3: Now Subtract That Integer )
Now we need to subtract the square of that integer (which equals 16) from the leftmost number (which equals 20). The result equals 4 and we will write it as shown above.
现在我们需要从最左边的数字(等于20)中减去该整数(等于16)的平方。 结果等于4，我们将如上所示将其写入。
步骤4：让我们移至下一对 (STEP 4: Let’s Move To The Next Pair)
Next, let’s move down the next pair in our number (which is 25). We write it next to the subtracted value already there (which is 4).
接下来，让我们向下移动数字中的下一对(25)。 我们将其写在已经存在的减法值旁边(即4)。
Now multiply the number in the top right corner (which is also 4) by 2. This results in 8 and we write it in the bottom right corner followed by _ x _ =
现在，将右上角的数字(也是4)乘以2。结果为8，我们将其写在右下角，后跟_ x _ =
步骤5：找到正确的匹配项 (STEP 5: Find The Right Match)
Time to fill in each blank space with the same integer (i). It must be the largest possible integer that allows the product to be less than or equal the number on the left.
用相同的整数(i)填充每个空白的时间。 它必须是最大可能的整数，以允许乘积小于或等于左侧的数字。
For example, if we choose the number 6, the first number becomes 86 (8 and 6) and we must also multiply it by 6. The result 516 is greater than 425, so we go lower and try 5. The number 8 and the number 5 give us 85. 85 times 5 results in 425, which is exactly what we need.
例如，如果我们选择数字6，则第一个数字变为86(8和6)，并且还必须将其乘以6。结果516大于425，因此我们走低并尝试5。数字8和数字5给我们85。85乘以5得到425，这正是我们所需要的。
Write 5 next to 4 in the top right corner. It is the second digit in the root.
在右上角的4旁边写下5。 它是根中的第二个数字。
步骤6：再次减去 (STEP 6: Subtract Again)
Subtract the product we calculated (which is 425) from the current number on the left (also 425). The result is zero, which means the task is complete.
从左侧的当前数字(也是425)减去我们计算出的乘积(即425)。 结果为零，表示任务已完成。
Note: I chose a perfect square (2025 = 45 x 45) on purpose. This way I could show the rules for solving square root problems.
注意：我故意选择了一个完美的正方形(2025 = 45 x 45)。 这样，我可以展示解决平方根问题的规则。
In reality, numbers consist of many digits, including the ones after the decimal point. In that case we repeat steps 4, 5 and 6 until we reach any accuracy we want.
实际上，数字由许多数字组成，包括小数点后的数字。 在这种情况下，我们重复步骤4、5和6，直到达到所需的精度为止。
The next example explains what I mean.
下一个示例解释了我的意思。
示例：我们进行更深入的研究… (EXAMPLE: We dig deeper…)
This time the number consists of an odd number of digits including the ones after the decimal point.
这次，数字由奇数个数字组成，包括小数点后的数字。
As we saw in this example, the process can repeat several times over to reach a desired level of accuracy.
正如我们在此示例中看到的那样，该过程可以重复几次以达到所需的精度水平。
翻译自: https://www.freecodecamp.org/news/find-square-root-of-number-calculate-by-hand/
无理数平方根计算
