Given :  √6.8  , root 6.8

To find : To be represented on Number LINE

Solution:

Step 1  : Draw a  Number  line

Step 2 : Take a point  A  at - 6.8  on  Number line

Step 3 : Using Appropriate Compass Width taking 1  & -6.8 as center draw arcs on both sides of number line intersecting at X & Y

Step 4 : Join X & Y  intersecting number line  at M    ( - 2.9 )   we could also directly take  -2.9   point

Step 5 :  Taking point M as center and compass width upto  A (-6.8)  or point 1 Draw a semicircle

Step 6 : Draw a right angle at  O (zero) on number line intersecting semicircle at  P

Step 7 :  Taking O (zero) as center & taking compass width = OP draw an arc intersecting number line on positive side at B

point B represent  √6.8  on number line

OP² =  ((6.8 + 1)/2)²  -  ((6.8 + 1)/2 - 1)²

= 3.9²  - 2.9²

= (3.9 + 2.9)(3.9 - 2.9)

= (6.8)(1)

= 6.8

=> OP = √6.8

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