CBSE Class 9 Answered
Let √x be any irrational number where x = 2, 3, 5, 6 … and so on.
Steps of Construction to represent √x on number line:
(1) Mark the distance x units from a fixed point O that represents 0 on the number line
(2) Mark a point P such that OP = x units.
(3) From P, mark a distance of 1 unit and mark this point as Q.
(4) Find the midpoint of OQ and name it as R.
(5) Taking QR as the radius, draw a semi circle.
(6) Draw a line perpendicular to OQ passing through P and intersecting the semi circle at S.
(7) Draw an arc with Center O and radius PS, which intersects the number line in T.
(8) Then, T represents the irrational number √x
We can represent many more irrational numbers on the same number line taking point P as (0) on the number line