The square root of 7 is not a rational number. A rational number is any number that can be expressed as the quotient or fraction p/q of two integers, with the denominator q not equal to zero. Since 7 is a prime number, its square root cannot be expressed as a simple fraction, and it is an irrational number.
To understand why, consider that if √7 were rational, it could be written as a/b where a and b are integers with no common factors other than 1. Squaring both sides gives 7 = a²/b², which implies a² = 7b². This means that a² is divisible by 7, and hence a must also be divisible by 7. Let a = 7k, then substituting back gives (7k)² = 7b², or 49k² = 7b², which simplifies to 7k² = b². This implies that b² is also divisible by 7, and hence b must be divisible by 7. But this contradicts our initial assumption that a and b have no common factors other than 1. Therefore, √7 cannot be rational.