The square root of 48 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 48 is not a perfect square, its square root cannot be expressed as a simple fraction.
To understand why, let’s break it down:
- The square root of 48 is approximately 6.928203230275509.
- This decimal does not terminate or repeat, which means it cannot be expressed as a fraction of two integers.
- Therefore, the square root of 48 is an irrational number.
In summary, the square root of 48 is not a rational number because it cannot be expressed as a fraction of two integers and its decimal representation is non-terminating and non-repeating.