Perfect Squares and Square Roots: The Case of 196 | 完全平方数与平方根：以196为例

📚 Perfect Squares and Square Roots: The Case of 196 | 完全平方数与平方根：以196为例

In IGCSE Mathematics, understanding square numbers and square roots is essential for many algebraic, geometric and number-based problems. The number 196 is a convenient starting point because it is a perfect square: 196 = 14².

在IGCSE数学中，理解平方数与平方根对于许多代数、几何和数论问题至关重要。数196是一个方便的起点，因为它是一个完全平方数：196 = 14²。

1. What is a Perfect Square? | 1. 什么是完全平方数？

A perfect square is an integer that equals the square of another integer. For example, 1 = 1², 4 = 2², 9 = 3², and 196 = 14².

完全平方数是一个整数，它等于另一个整数的平方。例如，1 = 1²，4 = 2²，9 = 3²，而196 = 14²。

Because 14 is a whole number, 196 is a perfect square. In fact, every integer multiplied by itself gives a perfect square: 0² = 0, 1² = 1, 2² = 4, and so on.

因为14是整数，所以196是完全平方数。事实上，任何整数与自身相乘都得到完全平方数：0² = 0，1² = 1，2² = 4，依此类推。

2. The Square Root Notation | 2. 平方根符号

The symbol √ denotes the non-negative square root of a number. If a² = N, then a is called a square root of N. In particular, √196 = 14, because 14 × 14 = 196.

符号√表示一个数的非负平方根。如果a² = N，那么a称为N的一个平方根。特别地，√196 = 14，因为14 × 14 = 196。

We also note that −14 × −14 = 196, so −14 is a square root as well. However, √196 is defined as the positive value 14.

我们还注意到−14 × −14 = 196，所以−14也是平方根。但√196被定义为正值14。

3. Square Numbers Up to 20 | 3. 20以内的平方数

Knowing the first 20 square numbers by heart will save you time in the exam. The table below lists each integer from 1 to 20 together with its square.

熟记前20个平方数能让你在考试中节省时间。下表列出了1到20每个整数及其平方。

Notice the highlighted row: 14² = 196. This row is the core example of the whole topic.

请注意高亮行：14² = 196。这一行是整个主题的核心例子。

4. Prime Factorisation Method | 4. 质因数分解法

To find √196 without a calculator, factorise 196 into primes. Divide by 2 twice and by 7 twice:

要在不用计算器

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