Question

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?
√50, √21, √13, √40

Answer 1

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:

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

Now rounding these values to the nearest whole number gives:

1. \( \sqrt{50} \approx 7.07 \) rounds to 7
2. \( \sqrt{21} \approx 4.58 \) rounds to 5
3. \( \sqrt{13} \approx 3.61 \) rounds to 4
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.