Final answer:
The expression √4 ⋅ √4 evaluates to 4, which is a rational number as it can be expressed as a fraction of two integers (4/1).
Step-by-step explanation:
To determine whether the expression √4 ⋅ √4 is a rational or irrational product, we must evaluate it. By definition, the square root of a number, such as √4, means the number which, when multiplied by itself, gives the original number. Hence, √4 is equal to 2, since 2 x 2 equals 4.
Now we multiply the square roots: √4 ⋅ √4 = 2 ⋅ 2 = 4. As 4 is a whole number and can be expressed as a fraction of two integers (4/1), it is a rational number. Therefore, the product of the given expression is rational.
It's important to eliminate terms wherever possible to simplify the algebra and then check the answer to see if it is reasonable as per A.5 Integer Powers and steps 6 and 7.