Question

Represent root3.9on the number line

Answer 1

To locate $\sqrt{3.9}$ on the number line.

Step 1: Draw a line say XY of length 3.9 cm.

Step 2: Now extend the line to a point say A by 1 cm.

Step 3: Now take your compass and take the length as the length of the line i.e., 3.9 cm + 1 cm = 4.9 cm. Mark the points on number line as shown.

Step 4: Now hold it on point X and make an arc as shown in the above attachment.

Step 5: Now hold it on point A and make an arc as shown in the above attachment.

Step 6: You'll observe that, both the arcs meet at a common point. Mark it as B.

Step 7: Now, draw a perpendicular line from point B to line XA. Mark the point as C.

Step 8: Now, take your compass on point C and draw a semicircle from point X to point A.

Step 9: Draw an arc on number line from C to Y.

Step 10: Now draw a perpendicular from point Y to the semicircle as shown in the above attachment. Mark the point as D.

Step 11: Take length in your compass as the length of line YD placing your compass over it. From D, draw an arc on number line. Mark the point as P.

Here, we've gotta our $\sqrt{3.9}$ on the number line.