Question

Represent $\sqrt 6 $ on number line.

Answer 1

Hint: According to the question we have to represent $\sqrt 6$ on the number line so first of all we have to draw a straight line and after that we have to mark a distance of 6 units considering a fixed point or we can say from a fixed point.
Now, mark the second point which we have taken 6 units and after that we have to mark a new point at a distance of 1 unit and we will obtain another point.
Now, we have to find out the midpoint of the two new points obtained then we have to mention that point.
Now, we have to draw a semicircle with respect to the midpoint as we obtained just above and then we have to draw a perpendicular that passes through intersecting the semicircle at any point and with the help of this point we can mark or represent $\sqrt 6 $ on the number line.

Complete answer:
Step 1: First of all we have to mark a distance of 6 units on the number line from a fixed point as mentioned in the solution hint, which we have already taken as A.

Hence, the length of AB = 6 units.
Step 2: Now, form the point B we have to take a distance of 1 unit as mentioned in the solution hint and then we will obtain a new point which is point C we can also understand it with the help of the diagram, as drawn below:

Step 3: Now, according to the solution hint we have to determine the midpoint of AC and we have to mark that point as the origin O. Hence,

Step 4: Now, we have to draw a semicircle with centre O and radius OC we can also understand it with the diagram as given below:

Step 5: Now, we have to draw a line perpendicular to line AC passing through B and intersecting the semicircle at point D.
Hence, BD= $\sqrt 6$ we can also understand the point $\sqrt 6$ on the number line with the help of the diagram as given below:

Note: To obtain the required number line it is necessary to mark the second point which we have taken 6 units and after that we have to mark a new point at a distance of 1 unit and we will obtain another point.