Maharashtra State BoardSSC (English Medium) 8th Standard
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Representation of Irrational Numbers on the Number Line

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Representation of Irrational Numbers on the Number Line:

Let us see how we can locate some of the irrational numbers on the number line.

1) Locate √2 on the number line.

Remember that √2 is the length of the diagonal of the square whose side is 1 unit.

 

  • On the number line, point A shows the number 1. Draw line `l` perpendicular to the number line through point A.
    Take point P on line `l` such that OA = AP = 1 unit. 
  • Draw seg OP. The ΔOAP formed is a right-angled triangle.
    By Pythagoras theorem, 
    OP2 = OA2 + AP2 = 12 + 12 = 1 + 1 = 2.
    ∴ OP = √2                ....(taking square roots on both sides)
  • Now, draw an arc with center O and radius OP. Name the point as Q where the arc intersects the number line. Obviously, distance OQ is `sqrt2`. 
    That is, the number shown by point Q is `sqrt2`. 
  • If we mark point R on the number line to the left of O, at the same distance as OQ, then it will indicate the number `- sqrt(2)`.
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