The square root of 3 (√3), point C, with an approximate value of 1.732, is the most suitable representation on the number line. Here option C is correct.
The value of 3 represents the positive square root of 9, indicating the distance from the origin (0) to the endpoint of a line segment with a length of 9 units on the number line.
To locate this point, the Pythagorean theorem is employed, stating that the square of the hypotenuse equals the sum of the squares of the other two sides in a right triangle.
Consider a right triangle with one side along the number line, starting from the origin and ending at the desired point. The perpendicular side, representing a vertical line, has a length of 0 units, and the hypotenuse connects the origin to the endpoint, with a length of 3 units. Applying the Pythagorean theorem:
3^2 = 9^2 + 0^2
Simplifying yields:
9 = 81 + 0
Subtracting 81 from both sides results in:
-72 = 0
This equation has no solution, indicating that none of the points (A, B, C, or D) accurately represents the value of 3 on the number line.
If the inquiry pertained to the square root of 3 (√3), the positive square root of 3, the scenario differs. The value of √3 is approximately 1.732, signifying the distance from the origin to the endpoint of a line segment with a length of 3 units on the number line. Utilizing a similar method with altered values:
√3^2 = 3^2 + 0^2
Simplifying yields:
3 = 9 + 0
Subtracting 9 from both sides results in:
-6 = 0
Once again, this equation lacks a solution. However, it's crucial to note that the square root of 3 (√3) can be approximated as 1.732. To locate the point on the number line corresponding to 1.732, one can use a ruler or compass to measure the distance from the origin to a point that is 1.732 units away.
According to my search results, point C on the number line accurately represents the value of 1.732, making it the best approximation for the square root of 3 (√3) among points A, B, C, and D¹². Hence, point C is the most suitable representation of the square root of 3 (√3) on the number line.