Question

how to represent root 19 in a number line without using the spiral method?

Answer 1

according to me there are two method only in our class 9 maths book .the first one is spiral method and the other one is used for representing decimal roots in the number line .

Answer 2

Solution:

To represent $\sqrt19$ on number line (without using the spiral method), following steps are to be followed:

Steps:

A distance of 19 units is to be marked from a fixed-point X on the number line.

A point Y is to be obtained, such that AB = 7 units.  

From Y a distance of 2 units is to be marked which is considered to be the new point Z.  

Then, the mid-point of XZ is to be located and marked as O.  

A semicircle with the centre O and radius OZ has to be drawn.

Then, a line perpendicular to XZ is to be drawn, that passes through Y and intersects the semicircle. This intersecting point is marked as A.  

Hence YA = $\sqrt19$  , where we treat YZ as the number line, with Y as 0, Z as 1, and so on.

Then an arc with the centre Y and radius YA, which is seen to intersect the number line.  

Thus, this point on the number line is $\sqrt19$