Question

Which numbers can be shown as squares?

Answer 1

Hint: Try to find the square of natural numbers. Hence from them obtain the square numbers. Try to give alternate explanations other than the arithmetic one.

Complete Step-by-Step solution:
Natural numbers are the positive numbers starting from one.
Squaring a number means multiplying the number by itself.
When you multiply a natural number of times itself, the resulting product is called a square number, or a perfect square or simply "a square."
 So, 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, and so on, are all square numbers.
As,
$
  1 \times 1 = 1 \\
  2 \times 2 = 4 \\
  3 \times 3 = 9 \\
  4 \times 4 = 16 \\
  5 \times 5 = 25 \\
$
It could also be thought of in a geometrical way.
Let 1 represent a square of side x.
Individually a single square is itself a square of side x.
If we combine 4 such squares, it results in a bigger square of side 2x. Hence, 4 is also a square number.
Similarly, by combining 9 such squares of side x, a bigger square of side 3x is formed, which implies 9 is also a square number.

Hence this trend can be continued and we can get the square numbers as:
1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144 and so on.
Hence the above numbers could be shown as the square numbers.

Note: The above square numbers which result from natural numbers are more specifically the positive integral numbers. Integers are the numbers having no decimal part or fractional part. Square numbers are also known as perfect squares.