Question

is √101 irrational because it is the square root of a non-perfect square, or because the decimal reapeats

Answer 1

√101 is irrational because it is the square root of a non-perfect square. Although the decimal representation of √101 is non-repeating, the decimal representation alone is not enough to determine the irrationality of a number. The fact that 101 is not a perfect square guarantees that √101 is an irrational number.