 Hello and welcome to the session. In this session we discussed the following question which says represent square root of 6.28 geometrically on the number line. Let's move on to the solution. We need to represent square root of 6.28 on the number line. For this, our first step is draw a line segment AB equal to 6.28 units. This is the line segment AB of measure 6.28 units. Then in the next step we extend AB to C such that we have BC is equal to 1 unit. So we have BC is equal to 1 unit. Then next we have this O is the midpoint of AC. That is we have AO is equal to OC is equal to half of AC which is equal to half of. Now AC is equal to AB plus BC that is 6.28 plus 1. So this is equal to half of 7.28 equal to 3.64 units. So we have AO equal to OC is equal to 3.64 units. Then in the next step with O as the center and radius as OA we draw a semicircle. So taking O as the center and radius equal to OA that is 3.64 units. We have drawn the semicircle. Then in the next step we draw BD perpendicular to AC. So this is BD perpendicular to AC such that this perpendicular is intersecting the semicircle at point D. Now consider this triangle over BD. This is the right angle triangle. So we apply Pythagoras theorem in this and we have OD square is equal to OB square plus BD square. This means BD square would be equal to OD square minus OB square. Now you see that OD is the radius of the semicircle. So this would be equal to OC which is equal to 3.64 units. And now OB would be equal to OC minus BC. Now again OC is the radii of the circle that is OC is equal to 3.64 units. And so we have this is equal to 3.64 minus BC which is the one unit. So this would be equal to 2.64 units. So we have OB is equal to 2.64 units. Thus we get BD square would be equal to OD square that is 3.64 square minus OB square which is 2.64 square. And this comes out to be equal to 6.28 that is we have BD square is equal to 6.28 which implies that BD is equal to square root of 6.28 units. So the length of this perpendicular BD is square root of 6.28 units. Now our next step is with B as the center and radius as BD we draw an arc. This is the arc drawn with B as the center and radius equal to BD which is square root of 6.28 and it needs AC produced at point E. Then we have BE is equal to BD is equal to square root of 6.28 units and hence we say the point E represents square root of 6.28. So this completes the session. Hope you understood the solution for this question.