Two points are shown on the number line.

Question

The image shows a number line with points F and G plotted at approximately 6.25 and 8, respectively.

The image is a simple line graph showing a number line ranging from approximately 5.5 to 8.5. The numbers 6, 7, and 8 are labeled below the line, marked by short vertical lines. There are additional unmarked short vertical lines to further subdivide the spaces between the labeled numbers. Two filled-in circles are placed on the line; one is labeled "F" and is located between 6 and 7, appearing to be closer to 6. The other circle is labeled "G" and is located between 7 and 8, closer to 8. The line extends beyond the marked numbers, with arrowheads at both ends to indicate that the number line continues infinitely in both directions. The overall mood is neutral and purely illustrative, relating to mathematical concepts.

Which value is best represented by the point G?
Responses
A square root of 7 point 9
B square root of 62 point 3
C square root of 65 point 8
D √54.9

Answer 1

To determine which value is best represented by the point G, which is located at approximately 8 on the number line, we will evaluate the approximate numerical values of the given options:

A. \( \sqrt{7.9} \approx 2.81 \)
B. \( \sqrt{62.3} \approx 7.9 \)
C. \( \sqrt{65.8} \approx 8.12 \)
D. \( \sqrt{54.9} \approx 7.4 \)

Since point G is approximately 8, the value that is closest to 8 from the options provided is option C, \( \sqrt{65.8} \approx 8.12 \).

So, the best answer is C \( \sqrt{65.8} \).