Question

Show the number √7 on the number line.

Answer 1

To represent √7​ on the number line, use the following construction:

1. Draw a number line and mark the points O(0), A(2), and B(3).
2. At point A, draw a perpendicular line AC of length √3​ units.
3. Join O to C. By the Pythagorean theorem,
   `OC = sqrt(2^2 + (sqrt3)^2)`
   `=sqrt(4+3)`
   `=sqrt7`
4. With O as the centre and radius OC, draw an arc that cuts the number line at point P.
5. The point P represents the number √7​​ on the number line.

Since √7 ​≈ 2.646, it lies between 2 and 3 on the number line.