CBSE Class 9 Answered

We will start by constructing surd 2.

First of all note that surd 2 is a hypotenuse of right angled triangle with both sides as 1. So start by drawing a length of 1 unit. Then using a protractor or compass draw a line perpendicular to it at the origin and cut off a length f 1 unit again. Now we have drawn two sides as OA and OB, Now AB  is equialent in magnitude to surd 2 and OA...  is the number line. Keep one end of compass at A and other oB and draw an arc which cuts the number line ahead of A at C. OC is equivalent to root 2.

Now note that root 3 ia hypotenuse of right angled triangle with sides as surd 2 (OC) and 1(OB).So similar to above surd 3 can be drawn. Following similar procedure and each time taking the next surd obtained as base keep obtaining the next surd as hypotenuse. This is the procedure for obtaining all the required surds.