True or False: Is the square root of 625 a rational number?
The correct answer and explanation is:
Correct Answer: True
The square root of 625 is a rational number.
Explanation (300 words):
To determine whether the square root of 625 is rational, we first need to understand what a rational number is.
A rational number is any number that can be written as a fraction (or ratio) of two integers. That means if a number can be expressed as a/b, where a and b are whole numbers and b ≠ 0, it is rational. Rational numbers include:
- All integers (since they can be written as themselves over 1, like 5 = 5/1),
- All fractions (like 3/4),
- All finite decimals (like 0.5),
- All repeating decimals (like 0.333…).
Now let’s look at the square root of 625: 625=25\sqrt{625} = 25
This is because: 25×25=62525 \times 25 = 625
Since 25 is a whole number, and whole numbers are a subset of integers, and integers can be written as fractions (e.g., 25 = 25/1), 25 is a rational number.
Therefore, the square root of 625 is rational because it simplifies to an integer, which qualifies as rational.
In contrast, if a number had a square root that resulted in a non-repeating, non-terminating decimal (like √2 ≈ 1.4142135…), then it would be irrational. But that’s not the case with 625.
Conclusion:
True – The square root of 625 is a rational number because it equals 25, which is a whole number and can be written as a fraction (25/1).