Question

how to draw √7 and √8.5 on number line

Answer 1

first draw a line. put points both positive and negative numbers . all points must be of equal length. take 90* on positive point 1. and draw a line equal to the points. draw a hypotenuse on that line through point 0 draw an arc through the above point and you will get
$\sqrt{2}$
and then draw another perpendicular of the same size of points and make another hypotenuse through point 0. and you will get √3 . go on until you get √7 and then stop. you will get √7 on the number line.



Sorry I cannot say next one cause I have to sent you a photo for that. see ya bye. please follow me. thank you dear.

Answer 2

Steps of construction for representating root 8.5 on a number line:

1) draw a line of 8.5 units. mark A as 8.5 and B as 0.

2) extend line segment AB 1 unit and mark it as C.

3) construct perpendicular bisector of AC and mark point of intersection as O.

4) with O as centre, and OA as radius, complete the semi-circle.

5) from the point B, construct a perpendicular, intersecting the semi-circle at D.

6) then, BD = root 8.5.

7) with B as centre and BD as radius, draw an arc, intersecting the number line as E.

E is a point root 8.5

PROOF:

AB = 8.5 unit

AC= 9.5 unit

OA = OC = 9.5/2, OD = 9.5/2

BC = 1 unit

OC= 9.5/2 unit

OB = OC - BC = 9.5/2 -1

therefore, ODsq = OBsq + BD sq (pythagorous theorem)

so, BD = root 8.5

HENCE, PROVED