show how under root 5 can be represented on the number line.

we draw a number line and mark the integers −2, −1, 0, 1, 2, 3, 4, etc. on it, so that the distance between any two consecutive integers is one unit. On this number line, we mark O and A at the points 0 and 2 respectively. At A, we draw AB of unit length which is perpendicular to OA. Now, we join OB. Taking O as the centre and OB as the radius, we will draw an arc which cuts the number line at P.

Now, point P represents the irrational numberon the number line. Let us verify it.

Using Pythagoras theorem in ΔOAB,

OB² = OA² + AB²

= 2² + 1²

= 4 + 1

= 5

But OP = OB

We know that,

And,

Mark a point ‘A’ representing 2 on number line. Now, construct AB of unit length perpendicular to OA. Then, taking O as centre and OB as radius, draw

an arc intersecting number line at C.

C is representing.

 this is the way........