To determine which of the given square roots could be the actual length of the diagonal of a square that measures approximately 7 inches, we can calculate the values of the expressions to see which one rounds to 7 inches when evaluated.
The formula for the diagonal \( d \) of a square with side length \( s \) is given by:
\[ d = s\sqrt{2} \]
Given that the diagonal is approximately 7 inches, we want:
\[ d \approx 7 \implies s\sqrt{2} \approx 7 \implies s \approx \frac{7}{\sqrt{2}} \approx 4.95 \]
Now we'll evaluate the square roots given:
- \( \sqrt{50} \approx 7.07 \)
- \( \sqrt{21} \approx 4.58 \)
- \( \sqrt{13} \approx 3.61 \)
- \( \sqrt{40} \approx 6.32 \)
Now rounding these values to the nearest whole number gives:
- \( \sqrt{50} \approx 7.07 \) rounds to 7
- \( \sqrt{21} \approx 4.58 \) rounds to 5
- \( \sqrt{13} \approx 3.61 \) rounds to 4
- \( \sqrt{40} \approx 6.32 \) rounds to 6
The only value that rounds to 7 is \( \sqrt{50} \).
Therefore, the actual length of the diagonal of the square could be \( \sqrt{50} \) inches.