The square root of 40 is not a rational number. A rational number is defined as a number that can be expressed as the quotient or fraction p/q of two integers, where p is the numerator and q is the non-zero denominator. The square root of 40, which is approximately 6.324555320336759, cannot be expressed as a simple fraction of two integers.
To understand why, let’s break it down:
- Prime Factorization: The number 40 can be factored into primes as 2 × 2 × 2 × 5, or 2³ × 5.
- Square Root Simplification: The square root of 40 can be simplified to √(2² × 2 × 5) = 2√10.
- Irrationality: Since √10 is an irrational number (it cannot be expressed as a fraction of two integers), multiplying it by 2 still results in an irrational number.
Therefore, the square root of 40 is an irrational number, not a rational one.