Not equal to Square of an integer

[swashbuckler]

Hi there I'm stumped on understanding the following answer in OG 11 PS Question 56

It states that (radical sign)4 = 2 is not the square of an integer.

Is 2 squared not 4

Why is this the case? I can't seem to find a detailed explanation for the rationale behind this.

[Ian Stewart]

4 is the square of an integer - it's the square of 2, and also the square of -2.

2, however, is not the square of an integer. It's the square of root(2), which is roughly 1.4, and of -root(2), which is roughly -1.4.

The OG is saying that 2 is not the square of an integer.

[swashbuckler]

Many thanks Ian for the explanation