HOW TO REPRESENT ROOT5 ON 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,

OB^{2} = OA^{2} + AB^{2}

= 2^{2} + 1^{2}

= 4 + 1

= 5

But OP = OB

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