Question

The Real Number System - 1/8
+0

Skill Review 1 of 6

Seiko is making a square poster. He wants to be sure that each side of the poster measures as a rational number. Which of the following values could be the area of Seiko's poster, in inches?

15
16
17
18

Answer 1

To determine which of the given values could be the area of Seiko's poster (a square), we need to recall that the area \( A \) of a square is calculated using the formula:

\[
A = s^2
\]

where \( s \) is the length of a side of the square.

For the area to be a rational number, \( s \) must be a rational number as well. Hence, \( A \) must be a perfect square, because the area of a square will only produce a rational value when taking the square root of a perfect square.

Now, let's evaluate the options provided:

1. **15**: Not a perfect square; \( \sqrt{15} \) is not a rational number.
2. **16**: Is a perfect square; \( \sqrt{16} = 4 \), a rational number.
3. **17**: Not a perfect square; \( \sqrt{17} \) is not a rational number.
4. **18**: Not a perfect square; \( \sqrt{18} \) is not a rational number.

The only area that is a perfect square and corresponds to a rational side length is:

**16**

Thus, the area of Seiko's poster could be 16 square inches.