Question

What is a perfect square?
Explain with an example.
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Answer 1

$\huge\red{Perfect ★ Square}$

$\huge\mathfrak\blue{Initial Definition}$

A perfect square is a number, from a given number system, that can be expressed as the square of a number from the same number system.

$\fbox\pink{Examples of Numbers}$

that are Perfect Squares ,25 is a perfect square.

25 is a natural number, and since there is another natural number 5, such that 52 = 25, 25 is a perfect square.

or

Since 25 is a natural number and the square root of 25 is a natural number (5), 25 is a perfect square.

$\fbox\blue{Divider Line}$

102.01 is a perfect square.

102.01 is a rational number, and since there is another rational number 10.1, such that (10.1)2 = 102.01, 102.01 is a perfect square.

or

Since 102.01 is a rational number and the square root of 102.01 is a rational number (10.1), 102.01 is a perfect square.

$\fbox\green{Divider Line}$

A perfect square fraction

Examples of Numbers that are NOT Perfect Squares

24 is NOT a perfect square.

24 is a natural number, but since there is no other natural number that can be squared to result in the number 24, 24 is NOT a perfect square.

or

Since 24 is a natural number, but the square root of 24 isn't a natural number (it's an irrational number that never terminates or repeats [4.898 979 486 ...]), 24 is NOT a perfect square.

$\fbox\purple{Divider Line}$

99.1 is NOT a perfect square.

99.1 is a rational number, but since there is no other rational number that can be squared to result in the number 99.1, 99.1 is NOT a perfect square.

or

Since 99.1 is a rational number, but the square root of 99.1 isn't a rational number (it's an irrational number that never terminates or repeats [9.954 898 292 ...]), 99.1 is NOT a perfect square

Answer 2

In mathematics, a square number or perfect square is an integer that is the square of an integer; in other words, it is the product of some integer with itself. For example, 9 is a square number, since it equals 32 and can be written as 3 × 3.