Final answer:
The decimal equivalent of √2 does not repeat but is non-terminating and non-repetitive, which classifies it as an irrational number, contradicting Lisa's claim.
Step-by-step explanation:
I disagree with Lisa's statement that √2 is irrational because its decimal equivalent will repeat. An irrational number is defined as a number that cannot be expressed as a fraction of two integers, and its decimal representation does not terminate or repeat. The square root of 2, or √2, is indeed an irrational number, but not because its decimals repeat; in fact, they never repeat and continue infinitely without a pattern. The decimal representation of irrational numbers is non-repetitive and non-terminating. Rational numbers, on the other hand, can always be expressed as a fraction between two integers and have decimal representations that either terminate or repeat.
Example of Rational Number
For example, the number ½ has a decimal representation of 0.5, which terminates, and ⅓, which equals approximately 0.333..., repeats indefinitely. Both are rational because they can be expressed as a fraction with integers as numerator and denominator.