how to locate irrational numbers on a number line
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Sure it is (though not all of them).
Using a compass and a ruler, you can represent square root of 2 in a number line.
Drawing the number line
Let's draw a line on a paper and mark zero in it, which we'll call O.
Pick any length of your choosing, let it be one unit.
Using the compass with this length as radius, mark of arcs in the line with this spacing. This is going to be 1,2,3....
Do this in the other side of zero as well.
Our number line is now ready. We have marked off (some) integers on it. We can also mark off any fraction using just a ruler and compass. But how do we mark an irrational number on the line?

Drawing a length of square root 2
From the 11 of the number line (which we'll call A), draw a perpendicular of height 11 unit. If you don't know how, please refer to this: How to construct (draw) a perpendicular at a point on a lineto draw the perpendicular line, and then use the compass to mark of 1 unit on this line, which we'll call point M.
Now, the distance between the points O and M is a hypotenuse of a right triangle with perpendiculars 1 unit long. This is 2–√2 in length.
Adjust your compass to this length and with O as the centre, draw a an arc on the number line. Mark this point P.
The point P is 2–√2 units away from zero, it is an irrational length unit.
Some extra info
While this is a simple proof of concept that you can draw line segments of irrational lengths units, it is actually not possible to draw any irrational length of your choosing using a compass and ruler alone. However, any fractional length can be drawn, though it might take a lot of precise drawing instruments, a steady hand, and a lot of patience.
There is a proof, for example, which shows that it is impossible to draw a length 213213 of a given length.
This page on wikipedia gives some impossible contractions using a ruler and compass and may be an interesting read.
Using a compass and a ruler, you can represent square root of 2 in a number line.
Drawing the number line
Let's draw a line on a paper and mark zero in it, which we'll call O.
Pick any length of your choosing, let it be one unit.
Using the compass with this length as radius, mark of arcs in the line with this spacing. This is going to be 1,2,3....
Do this in the other side of zero as well.
Our number line is now ready. We have marked off (some) integers on it. We can also mark off any fraction using just a ruler and compass. But how do we mark an irrational number on the line?

Drawing a length of square root 2
From the 11 of the number line (which we'll call A), draw a perpendicular of height 11 unit. If you don't know how, please refer to this: How to construct (draw) a perpendicular at a point on a lineto draw the perpendicular line, and then use the compass to mark of 1 unit on this line, which we'll call point M.
Now, the distance between the points O and M is a hypotenuse of a right triangle with perpendiculars 1 unit long. This is 2–√2 in length.
Adjust your compass to this length and with O as the centre, draw a an arc on the number line. Mark this point P.
The point P is 2–√2 units away from zero, it is an irrational length unit.
Some extra info
While this is a simple proof of concept that you can draw line segments of irrational lengths units, it is actually not possible to draw any irrational length of your choosing using a compass and ruler alone. However, any fractional length can be drawn, though it might take a lot of precise drawing instruments, a steady hand, and a lot of patience.
There is a proof, for example, which shows that it is impossible to draw a length 213213 of a given length.
This page on wikipedia gives some impossible contractions using a ruler and compass and may be an interesting read.
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