SOLUTION: please help me solve this problem i do not understand what they mean. If the square root of a number is a repeating decimal, is the square root a rational number? thank you

Question 527530: please help me solve this problem i do not understand what they mean. If the square root of a number is a repeating decimal, is the square root a rational number?
thank you
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
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

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