Plotting any Irrational Numbers On a Number Line
Plotting any Irrational Numbers On a Number Line
Plotting any Irrational Numebrs On a Number Line:
For any positiv real number x, we have
Therefore, to find the positive square root of a positive real number, we may follow the following algorithm.
ALGORITHM:
STEP I Obtain the positive real number x(say)
STEP II Draw a line and mark a point A on it.
STEP III Mark a point B on the line such that AB = x units.
STEP IV From point B mark a distance of 1 unit and mark the new poiint as C.
STEP V Find the mid-point of AC and mark the point as O.
STEP VI Draw a circle with centre O and radius OC>
STEP VII Draw a line perpendicular to AC passing through B and intersecting the semi-circle at D. Length BD is equal to
Justification: We have,
AB = x units and BC = 1 unit.
AC = (x + 1) units
Now,
Using Pythagoras Theorem in we have
This shows that exists for all real numbers x > 0.
In order to find the position of on the number line, we consider BC as the number line, with B as the origin to represent zero. Since BC = 1 so, C represents 1. Now, mark points
such that
= 1,
and so on. Clearly,
represent 2, 3, 4,... respectively.
Now, draw an arc with centre at B and radius equal to BD. Suppose this arc cuts the number line BC with B as the origin at E. Then, BE = . Consequently, E will represent
.
Is it possible to say that | |||
| Right Option : B | |||
| View Explanation | |||
Can all irrational numbers be plotted on a number line? | |||
| Right Option : B | |||
| View Explanation | |||
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