Show how √5 can be represented on the number line.

To represent the value of root 5 (√5) on the number line, we need to follow a geometric construction method. It involves using the Pythagoras Theorem and constructing a right triangle to find the precise location of √5 on the number line.

Steps to Represent √5 on the Number Line:

Step 1: Start by marking the point 2 units from 0 on the number line. Label this point as A. The distance between 0 and A represents 2 units, i.e., the segment AB = 2 units.

Step 2: At point B, draw a perpendicular line and mark the point C such that the distance BC = 1 unit. Now, connect points A and C. This will form a right-angled triangle ABC, with AC as the hypotenuse. Using the Pythagoras Theorem, we can calculate the length of the hypotenuse AC.

According to the Pythagorean theorem: 
AC² = AB² + BC² 
AC² = 2² + 1² = 4 + 1 = 5 
AC = √5 units

Thus, we can conclude that the hypotenuse AC represents the value of root 5 (√5).

Step 3: Now, with point A as the center and the length of the hypotenuse AC as the radius, draw an arc with radius AC. This arc will intersect the number line at point D. Since AC = AD = √5 units, the point D represents the value of √5 on the number line.

Conclusion

By following these steps, we can accurately represent the value of root 5 (√5) on the number line. This method involves constructing a right triangle and applying the Pythagoras Theorem to find the hypotenuse, which gives us the value of √5