How to draw 15 on number line

Asked by Jayanth | 21st Sep, 2015, 07:40: PM

Expert Answer:

begin mathsize 14px style Let space us space first space find space square root of 13 open parentheses square root of 13 close parentheses squared equals open parentheses square root of 9 close parentheses squared plus open parentheses square root of 4 close parentheses squared Hence comma space construct space increment OAB space on space number space line comma space as space shown space in space the space figure. In space increment OAB comma space OA perpendicular OB therefore open parentheses OB close parentheses squared space equals open parentheses OA close parentheses squared space plus open parentheses AB close parentheses squared space space space space open parentheses Pythagoras close parentheses therefore open parentheses OB close parentheses squared space equals 3 squared space plus 2 squared equals 13 comma space therefore OB space equals space square root of 13 Draw space an space arc space of space radius space OB space taking space straight O space as space the space centre. The space arc space intersects space the space number minus line space at space square root of 13 Let space us space now space find space square root of 14 open parentheses square root of 14 close parentheses squared equals open parentheses square root of 13 close parentheses squared plus open parentheses square root of 1 close parentheses squared therefore Taking space OB space as space the space base space and space BC perpendicular OB comma space construct space BC space of space length space 1 space unit. In space increment OBC comma space therefore open parentheses OC close parentheses squared space equals open parentheses OB close parentheses squared space plus open parentheses BC close parentheses squared space space space open parentheses Pythagoras close parentheses therefore open parentheses OC close parentheses squared space equals 13 space plus 1 equals 14 comma space therefore OC space equals space square root of 14 Draw space an space arc space of space radius space OC space taking space straight O space as space the space centre. The space arc space intersects space the space number minus line space at space square root of 14 Let space us space now space find space square root of 15 open parentheses square root of 15 close parentheses squared equals open parentheses square root of 14 close parentheses squared plus open parentheses square root of 1 close parentheses squared therefore Taking space OC space as space the space base space and space DC perpendicular OC comma space construct space DC space of space length space 1 space unit. In space increment ODC comma space therefore open parentheses OD close parentheses squared space equals open parentheses OC close parentheses squared space plus open parentheses DC close parentheses squared space space space open parentheses Pythagoras close parentheses therefore open parentheses OD close parentheses squared space equals 14 space plus 1 equals 15 comma space therefore OD space equals space square root of 15 Draw space an space arc space of space radius space OD space taking space straight O space as space the space centre. The space arc space intersects space the space number minus line space at space square root of 15 equals space 3.87 end style
 

Answered by Priti Shah | 22nd Sep, 2015, 01:01: PM