Question

A student says that the square root of 7 is a rational number because it can be written as [The square root of 7] over 1. Is the student correct? explain

Answer 1

Let's start by defining what a rational number is. It is a number that is expressed as a fraction. It could also be in decimal form, but only in circumstances when the decimal places are exact and not continuous or repeating. Let's take for example √7. Its exact value is 2.645751311. The decimals places are random and continuous that's why it can't be expressed into fraction. But if the decimal for is, say, 0.25, that is rational because it can be expressed to 1/4.

Now, the reason where it could be a fraction by using a denominator of 1 is invalid. All whole numbers have a denominator of 1. It is implicitly defined because any number divided by 1 is equal to the number itself. This is not a basis for a characteristic of a rational number. Therefore, the student is incorrect.