Question

Number lines are important because they present numbers in real life. We know how to plot natural, whole, integers and rational numbers on real number line but irrational numbers are vital part of real numbers. Is there any way of plotting irrational numbers on real numbers? If answer is yes, then plot below numbers on number line and write steps of construction.

1. √2

2. 2+√3

3. √45

4. π

5. √3/2







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Answer 1

Answer:

It takes very lot of time

Step-by-step explanation:

Answer 2

Answer:

Yes, It is possible to plot irrational numbers on number line.

Step-by-step explanation:

To plot irrational numbers on a number line,
We need to follow following steps.

Step 1 :

• Draw a number line.
• Mark the center point as zero.
• Mark points 1 and -1 on either sides of zero on number line with same distance between zero and 1 or -1.
• For the time being ignore point -1.

Step 2 :

• Draw a perpendicular line from point 1 of same length as between 0 and 1.
• Name the point as A.
• Connect 1 and A and 0 and A.
• Let point 0 be B and point 1 be C
• Thus, figure ABC forms a right angled triangle with adjacent sides measuring 1 units.

Step 3 :

• For triangle ABC, being a right angled triangle, use Pythagoras theorem.
• Accordingly,

$(AB)^{2} = (AC)^{2} +(BC)^{2}$

∵$(AB)^{2} =1^{2} +1^{2}$

∴$(AB)^{2} =1 + 1$

∴ $(AB)^{2} =2$

∴ $AB = \sqrt{2}$

Step 4 :

• Now consider AB as the radius of length $\sqrt{2}$ units.
• Measure length $\sqrt{2}$ on compass and draw an arc on the number line considering point B as the center and mark the point as point D.
• Since AB measures $\sqrt{2}$ units, AD will also measure $\sqrt{2}$ units.

Step 5 :

• Thus we got a point measuring $\sqrt{2}$ units on the number line.
• Similarly, we can plot different irrational numbers on the number line following the steps mentioned above.

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