represent root 7.5 on the number line

Dear Student, 
Solution)
We follow these steps to represent  $\sqrt{7.5}$ on number line :

Step 1 :  Draw a line AB  =  7.5 unit

Step 2 : Now extend line AB , As BC  =  1 unit

Step 3 : Take radius more than half of AC and centre "  A " and " C " draw two arcs from both points on both side of line AC , these arcs intersect at " X " and " Y " . .

Step 4 : Join XY . Line XY intersect line AC at  " O " . Take radius OA = OC and draw a semicircle .

Step 5 : Take any radius ( less than BC ) and centre " B "  draw a semicircle that intersect line AC at " P " . Now with same radius and centre " P " draw an arc that intersect our semicircle at " Q " .With same radius and centre " Q " draw an arc that intersect our semicircle at " R " .With same radius and centre " Q " and " R "  draw  arcs these arcs intersect  at " S " .

Step 6 : Join BS and extend that line intersect our main semicircle at " D " .

Step 7 :  Now we take point " B " at origin . and with radius of BD we draw an arc that intersect our number line at " D " . We represent $\sqrt{7.5}$ at " D " .


Regards!