Plotting Irrational Numbers on a Number Line as a Spiral


 
 
Concept Explanation
 

Plotting Irrational Numbers on a Number Line as a Spiral

While plotting an irrational number we will be using Pythagoras theorem. It state the relationship between the sides of the right angled triangle. Let us have a look at the. Delta ABC  is a right triangle, right angled at B, so that AC is the hypotenuse and AB and BC are the sides of the right triangle,

Then,                    (AC)^{2}=(BC)^2+(AB)^2

i.e.,                 (Hypotenuse)^{2}=(Base)^{2}+(Perpendicular)^{2}

If AB = BC = 1 unit  then

(AC)^{2}=1^2+1^2= 1+ 1= 2

Rightarrow AC=sqrt 2

Using this relation we can plot sqrt 2 on the number line

Plotting any Irrational Numbers On a Number Line as a Spiral

Draw a number line and mark a point C, representing zero, on it. Suppose point B represents 1 unit as shown in fig. Then,BC = 1. Now, draw a right triangle ABC such that BC = AB = 1.

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Sample Questions
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Question : 1

In A Right triangle ABC ,right angled at B. Given that BC=1,AC=sqrt2. then what will be the AB ?

Right Option : D
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Question : 2

In a right triangle ABC , right angled at B. Given that AB= sqrt3 , BC=1. Find out the AC.

Right Option : C
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Explanation
Question : 3

In a right angle triangle ABC , right angled at B .Given that  AB =sqrt2 , BC=1. Find out the value of AC.

Right Option : C
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Explanation
 
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