How to draw root 3 and root 5 on a number line?

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Earlier we discussed how to draw root 2 on a number line, in this article we will discuss How to draw root 3 and root 5 on a number line. It is necessary to learn how to draw root 2 on a number line and should also know about the Pythagorean theorem to learn this. Read this article to know about how to draw root 2 on a number line. and the Pythagorean theorem.

Inside Story

How to draw root 3 and root 5 on a number line?

To draw these irrational numbers on the number line, one should take a ruler, compass, and pencil. First, we will learn How to draw root 3 on a number line then we will move to root 5.

How to draw root 3 on the number line?

Theory:

For √3, we can assume a triangle with B=√2, P=1 then it gives $$\text{B=√2, P=1 then}$$ $$H^2=P^2+B^2$$ $$H^2=√2^2+1^2=3$$ $$H=\sqrt{3}$$

Construction:

Step 1: Draw a number line.

Step 2: Draw the root 2 on the number line.

Step 3: Draw a line perpendicular to the hypotenuse of the drawn triangle.

Step 4: Take a compass, place its tip on the 0 and the pencil on the tip of the perpendicular line, move the compass downwards and mark the cut on a number line.

The distance 0 to Q is √3

How to draw root 5 on the number line?

Theory:

For root 5, we can assume a triangle with B=2, P=1 then it gives $$\text{B=2, P=1 then}$$ $$H^2=P^2+B^2$$ $$H^2=2^2+1^2=5$$ $$H=\sqrt{5}$$

Construction:

Step 1: Draw a number line.

Step 2: Now draw a line of 1cm perpendicular to the number line at point 2.

Step 3: The hypotenuse of this right-angled triangle is √5.

Step 4: Now cut an arc with the help of a compass to draw root 5 on a number line.

Conclusion

We can learn How to draw root 3 and root 5 on a number line, with the help of a ruler, compass, and pencil. One should have the knowledge of Pythagoras’s theorem to understand the logic behind its construction.

To learn How to draw root 3 on a number line, we constructed a right-angle triangle with the base of √2 and perpendicular as 1. \

To learn How to draw root 5 on a number line, we constructed a right-angle triangle with a base of 2 and a perpendicular of 1.

We hope the article helped you. Feel free to ask your doubts in the comment section.

What are the instruments we need to draw root 3 and root 5 on the number line?

Compass, ruler, and pencil

What is the prerequisite to learning the construction of root 3 and root 5 on the number line?

One should have a basic knowledge of geometry, should know how to draw √2 on a number line. and the Pythagorean theorem

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