to the nearest whole number, the length of the diagonal of a square is 7 inches. which measure could be the actual length in inches of the diagonal of the square?

Question

square root of 50
square root of 40
square root of 13
square root of 21

Answer 1

To find which measure could be the actual length of the diagonal of the square, we will calculate the approximate values of the given lengths:

1. \( \sqrt{50} \approx 7.07 \)
2. \( \sqrt{40} \approx 6.32 \)
3. \( \sqrt{13} \approx 3.61 \)
4. \( \sqrt{21} \approx 4.58 \)

The problem states that the length of the diagonal is 7 inches when rounded to the nearest whole number. Thus, the actual length of the diagonal must be between 6.5 inches and 7.5 inches.

Now, we compare the calculated values to this range:

• \( \sqrt{50} \approx 7.07 \) (within the range)
• \( \sqrt{40} \approx 6.32 \) (not within the range)
• \( \sqrt{13} \approx 3.61 \) (not within the range)
• \( \sqrt{21} \approx 4.58 \) (not within the range)

The only value that fits the criteria, being within the range of 6.5 to 7.5 inches, is:

\( \sqrt{50} \).