Which numbers are rational? Check the three that apply.

A. \sqrt(32)
B. 12/17
C. \sqrt(16)
D. \sqrt(70)
E. pi
F. 4.52525252...

1 answer

A rational number is any number that can be expressed as a fraction \( \frac{a}{b} \), where \( a \) and \( b \) are integers and \( b \neq 0 \).

Let's analyze the options provided:

A. \( \sqrt{32} \) - This is an irrational number since it cannot be expressed as a fraction of integers.

B. \( \frac{12}{17} \) - This is a rational number because it is already in the form \( \frac{a}{b} \).

C. \( \sqrt{16} \) - This is equal to 4, which is a rational number since it can be expressed as \( \frac{4}{1} \).

D. \( \sqrt{70} \) - This is an irrational number since it cannot be expressed as a fraction of integers.

E. \( \pi \) - This is an irrational number.

F. \( 4.52525252... \) - This is a repeating decimal, which can be expressed as a fraction, making it a rational number.

Based on this analysis, the numbers that are rational are:

B. \( \frac{12}{17} \), C. \( \sqrt{16} \), and F. \( 4.52525252... \).