Question

it has been demonstrated that \\(\sqrt{53}\\) is between 7.28 and 7.29. if we were to continue this process, it would because \\(\sqrt{53}\\) is .

Explanation:

Step1: Recall the nature of irrational numbers

Irrational numbers are numbers that cannot be expressed as a fraction of two integers and have non - repeating, non - terminating decimal expansions. $\sqrt{53}$ is an irrational number because 53 is a prime number, and the square root of a prime number is irrational.

Step2: Analyze the process of approximating $\sqrt{53}$

When we approximate $\sqrt{53}$ (for example, by using the method of successive approximation or the decimal expansion method), since it is an irrational number, its decimal expansion never terminates and never repeats. So if we were to continue the process of approximating $\sqrt{53}$ (finding more and more decimal places), it would never end because $\sqrt{53}$ is irrational (or has a non - terminating, non - repeating decimal expansion).

Answer:

The first blank: never end; The second blank: irrational (or has a non - terminating, non - repeating decimal expansion)