 Hello and welcome to the session. In this session, we are going to discuss the following question which says that represent square root of 9.3 on the number line. Now let us start with the solution. Now to represent square root of 9.3 on the number line, we will follow these steps of construction which we are going to discuss one by one. And first, we mark the distance that is 9.3 units from a fixed point A and obtain a point B such that A B is equal to 9.3 units. So here we have the line segment A B which is equal to 9.3 units. Now from B, we mark a distance of 1 unit and mark the new point as C that is here from the point B, we mark a distance of 1 unit and we name this new point as C and therefore we get the line segment B B which is equal to 1 unit. Now we find the midpoint of the line segment AC and name it as N. So now we have point N as the midpoint of the line segment AC. So we can say that the line segment AM is equal to the line segment MC. Now taking MC as radius and point M as centre, we draw a semicircle that is here taking the line segment MC as radius and point M as centre. We have drawn a semicircle. Now we draw a line perpendicular to AC passing through the point B and intersecting the semicircle at point D and the angle DBC should be equal to 90 degrees as DB is perpendicular to AC. Now in triangle MDB, here we should note that DB is perpendicular to the line segment AC. So by Pythagoras theorem we can say MD square is equal to MV square plus DB square. Now AM is equal to MC since M is the midpoint of the line segment AC. So we can write AM is equal to MC and is equal to AC by 2 and we know that AC is given by AB plus BC that is 9.3 plus 1 over 2 and it is equal to 10.3 by 2 also MB can be written as MC minus of BC that is we know that MC is equal to 10.3 by 2 and BC is given by 1. So on taking LCM this is equal to 10.3 minus 2 whole upon 2 which is equal to 8.3 by 2. Also we know that MD is the radius of the semicircle at MC and therefore it is equal to 10.3 by 2. Now we know the values of MD and MB and on putting these values in this equation we can calculate the value of DB as DB square will be given by MD square minus MB square and this is equal to MB square that is 10.3 by 2 whole square minus of MB square that is 8.3 by 2 whole square and this is equal to 9.3 so we say that DB square is equal to 9.3 implies that DB is equal to square root of 9.3 and then we draw an arc with center B and radius BD which intersects the number line in point E that is here we treat point B as 0, point C as 1 and so on Now with center B and radius BD we have drawn an arc which intersects the number line at point E and E is the required point which represents square root of 9.3 on the number line thus we have represented square root of 9.3 on the number line This completes our session, hope you enjoyed this session