Final answer:
Alijah is correct; the square root of 64 is 8, which is a rational number since it can be expressed as a fraction 8/1. Irrational numbers, unlike 8, cannot be expressed as fractions and have non-repeating decimal parts.
Step-by-step explanation:
Alijah is correct in saying that the square root of 64 is a rational number. A rational number is any number that can be expressed as the quotient of two integers, where the denominator is not zero. In the case of the square root of 64, we can calculate it as √64 which equals 8. Since 8 can be expressed as 8/1, which is the quotient of two integers (8 and 1), it is indeed a rational number. Jay's claim that it is an irrational number is incorrect because irrational numbers are numbers that cannot be expressed as a simple fraction; they have endless non-repeating decimal parts, such as π (pi) or the square root of 2.
The concept of rational numbers, irrational numbers, and square roots are fundamental in mathematics. It's important to remember that square roots of perfect squares (like 64, which is 8 squared) always result in rational numbers, whereas square roots of non-perfect squares result in irrational numbers. This is because the square root of a perfect square can always be simplified to an integer or a simple fraction.