Which product is rational?
A. 10 • √8
B. 12 • π
C. 12 • 5.3420941....
D. 8 • √25
D. 8 • √25
To determine which product is rational, we need to identify which option can be represented as a ratio of two integers.
A. 10 • √8 = 10 • √(4 • 2) = 10 • (2 • √2) = 20 • √2. Since √2 is irrational, this option is not rational.
B. 12 • π is the product of an integer and an irrational number (π), so it is not rational.
C. 12 • 5.3420941.... is the product of an integer and a decimal number. Decimal numbers can be rational or irrational, depending on whether they terminate or repeat. Without knowing the sequence of digits after the decimal point, we cannot definitively determine if this option is rational or irrational.
D. 8 • √25 = 8 • 5 = 40. Since 40 can be represented as the ratio 40/1, this option is rational.
Therefore, the only product that is clearly rational is D. 8 • √25.