Is √7 a Rational or Irrational Number?
Understanding the Nature of √7:
√7 represents the square root of 7. In other words, it is the number that, when multiplied by itself, gives the result of 7.

Rational Numbers:
Rational numbers are those that can be expressed as a ratio of two integers. This includes fractions and integers.

Irrational Numbers:
Irrational numbers cannot be expressed as a simple fraction. They are non-repeating and non-terminating decimals.

Analysis of √7:
To determine whether √7 is rational or irrational, we need to consider whether it can be expressed as a ratio of two integers.
If √7 were rational, it could be expressed as a fraction a/b where a and b are integers, and b is not equal to 0.

Proof by Contradiction:
Assume that √7 is rational and can be expressed as a fraction a/b.
√7 = a/b
Squaring both sides, we get:
7 = (a^2) / (b^2)
This implies that 7b^2 = a^2. Therefore, a^2 is a multiple of 7, making a a multiple of 7 as well.
Since a is a multiple of 7, a^2 is a multiple of 49.
This contradicts our assumption that a^2 = 7b^2, proving that our initial assumption that √7 is rational is false.

Conclusion:
Since our assumption leads to a contradiction, we can conclude that √7 is an irrational number. It cannot be expressed as a simple fraction and has a non-repeating, non-terminating decimal representation.