Question 527530
Yes. Repeating decimals are rational numbers, so the square root of the number, and the number itself, are rational.


To prove that a repeating decimal is rational, you can treat an iterating "string" of digits as a term of a geometric series. For example, if your repeating decimal is 0.034034034... you can let the "string" be 034, in which the corresponding geometric series would be


*[tex \LARGE \sum_{i=1}^{\infty} 34(10^{-3k})]


If you know the formula for the sum of a convergent geometric series, you can conclude that this is rational.