Given :   root 4 .1     √4.1

To find  : represent on NUMBER line

Solution:

Step 1  :  Draw a number line  AOB    ( O being 0)

Step 2 : Take a length of 4.1 cm from O on left side mark it M

Step 3 : Take 1 cm from O on right side  , mark it N

Step 4 : Using suitable compass width draw arcs on both sides of MN taking M & N as center & intersecting at X & Y

Step 5 : join X & Y intersecting MN at  P  

Step 6 :  Draw a semicircle taking P as center & PM = PN as radius ( compass width)

Step 7 : Draw a right angle at AO  such that it intersect semicircle at  Z

OZ = √4.1

Step 8 : Taking compass width = OZ  and taking O as center  cut the number line on right side at C

point C  represent  √4.1 on a number line

Mathematical proof

Semicircle radius  =  (4.1 + 1)/2  =  5.1/2  ( hypotenuse)

5.1/2 - 1  = 3.1/2  = Base

Perpendicular OZ²  =( 5.1/2)² - (3.1/2)²

=>  OZ²  = (5.1/2 + 3.1/2) (5.1/2 - 3.1/2)

=> OZ²  = 4.1

=> OZ = √4.1

Learn more:

1. Represent 7, 7.2,-3/2,-12/5 on number line​ - Brainly.in

brainly.in/question/10782917

represent each of the following numbers on the number line 1/3 ...

brainly.in/question/9092964

brainly.in/question/6101797