Final answer:
√(5/25) is a rational number because it simplifies to 1/5, which is a quotient of two integers (1 and 5) with the denominator not being zero.
Step-by-step explanation:
The question is asking whether the square root of the fraction 5/25 is a rational number. A rational number is a number that can be expressed as the quotient of two integers. To find the square root of 5/25, we can take the square root of both the numerator and the denominator separately since the square root of a fraction is the square root of the numerator over the square root of the denominator.
The square root of 5 is irrational, but we do not actually need to find its value. The square root of 25 is 5, since 5 multiplied by itself yields 25. Therefore, the square root of 5/25 simplifies to √5/5. Since 5 is a perfect square and its square root is an integer, we can simplify further:
√5/5 = √5/√25 = √5/5 = 1/√5
However, 1/√5 is not an integer because the square root of 5 is not an integer. Nevertheless, we can rationalize the denominator by multiplying both the numerator and the denominator by √5, resulting in:
1/√5 × √5/√5 = √5/5
This gives us the initial fraction √5/5, which simplifies to 1/5, a rational number, since both 1 and 5 are integers and 5 is not zero. Consequently, the answer to the question is (a) Yes, √(5/25) is a rational number.