Question

The Real Number System - 1/6
+0

Skill Review 1 of 4

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


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1,019
1,117
1,296
1,386

Answer 1

To determine which of the following values could be the area of Uri's square platform, we need to remember that the area \( A \) of a square is calculated by the formula:

\[
A = s^2
\]

where \( s \) represents the length of one side of the square. For the area \( A \) to be a value whose square root \( s \) is a rational number, the area must be a perfect square.

Let's evaluate each given area to see if it is a perfect square:

1. **1,019**
- \( \sqrt{1,019} \) is approximately 31.95 (not a whole number, not a perfect square).

2. **1,117**
- \( \sqrt{1,117} \) is approximately 33.5 (not a whole number, not a perfect square).

3. **1,296**
- \( \sqrt{1,296} = 36 \) (which is a whole number, and thus a perfect square).

4. **1,386**
- \( \sqrt{1,386} \) is approximately 37.21 (not a whole number, not a perfect square).

Based on this analysis, the only value that could be the area of Uri's platform, ensuring that each side measures a rational number, is:

**1,296** (which equals \( 36^2 \)).