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2015-04-02T19:48:17+05:30
Draw  a line AB  of the number which  has been given  to be  represented .  if  your  give to represent  square root of 8 then  make a line of 8 cm. and using a  compass bisect this line AB  and then make semicircle from  the  point  of intersecting   of the bisect  using a compass.  and then take a  potactor and  draw an angle of 90 degree  of the point from  where the line was extenden . the line where meet the  semicircle is equal to under root 8..........
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2015-04-02T21:03:11+05:30

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I suppose we can use the ruler, scale, protractor, compass...

there are possibly two ways.

     2² + 2² = 8 = (√8)² 
So construct a right angle triangle with two sides equal to 2 units, then the hypotenuse will be of  √8 units.

   Draw a long horizontal line AD.  Draw a perpendicular AE at A.  Bisect the angle DAE to draw the line AF which is at 45⁰ to AD.  Now with compass measure 2 units and draw an arc with center A intersecting AF at B. So AB = 2 units. 
   Now with B as the center and with compass draw an arc cutting AD at C.  So BC = 2 units.  Thus we get  AC = √8  units - on the horizontal real line.

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2nd way

   3² - 1² = 8 =  (√8)² 
    construct a right angle triangle with a side = 1 unit, and the hypotenuse = 3 units, then the other side is √8 units.  

   Draw a long horizontal line AD.  At point A, draw AE vertically at 90° to AD.  Now with compass set = 1 unit, draw an arc with center A to cut AE at B.  So AB = 1.

You may use the compass, protractor and ruler, right?   Now, measure 3 units with the compass.  Draw an arc with center as B, to cut AD at C.  So AC = 3 units.  Thus  BC = √8 units on the horizontal real number line.

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