What are perfect squares and their properties as outlined in the CBSE Class 8 Mathematics revision notes?

Steps to Solve

1. Understanding Square Numbers

A square number is obtained when a natural number is multiplied by itself. Mathematically, for a natural number $n$, the square number can be expressed as $m = n^2$.

2. Identifying Perfect Squares

A perfect square number requires that there exists a natural number $n$ such that $m = n^2$. For example, if $n = 3$, then $3^2 = 9$ gives a perfect square number.

3. Properties of Square Numbers

Square numbers have specific properties:

• They end in 0, 1, 4, 5, 6, or 9 at the unit's place.
• They can only have even numbers of zeros at the end.
• If a number ends in digits like 2, 3, 7, or 8, then it can't be a perfect square.

4. Square Root Notation

The positive square root of a number is denoted by the symbol $\sqrt{n}$. For example, the positive square root of 9 is $\sqrt{9}=3$.

5. Examples of Square Numbers

To reinforce understanding, several examples can be provided:

• If $n = 4$, then $n^2 = 4 \times 4 = 16$ (16 is a perfect square).
• If $n = 5$, then $n^2 = 5 \times 5 = 25$ (25 is a perfect square).