Question

how to show the number
$\sqrt{2}$
on a number line.​

Answer 1

root numbers also known as irrational numbers on the number line. Before going on the topic, let’s understand a simple concept of Pythagoras Theorem, which states that:

“if ABC is a right angled triangle with AB, BC and AC as the perpendicular, base and hypotenuse of the triangle respectively with AB = x units and BC = y units. Then, the hypotenuse of the triangle, AC is given by x2+y2−−−−−−√x2+y2

Irrational Numbers

Now lets get back to the original topic , i.e., representation of irrational numbers on the number line.

To have better understanding of the concept lets take an example of representation of square root of 2 (2–√2) on the number line. For the representation following steps must be followed:

Step I: Draw a number line and mark the centre point as zero.

Step II: Mark right side of the zero as (1) and the left side as (-1).

Irrational Numbers Number Line

Step III: We won’t be considering (-1) for our purpose.

Step IV: With same length as between 0 and 1, draw a line perpendicular to point (1), such that new line has a length of 1 unit.

Step V: Now join the point (0) and the end of new line of unity length.

Step VI: A right angled triangle is constructed.

Step VII: Now let us name the trianlge as ABC such that AB is the height (perpendicular), BC is the base of triangle and AC is the hypotenuese of the right angled triangle ABC.

Square Root of 2

Step VIII: Now length of hypotenuse, i.e., AC can be found by applying pythagoras theorem to the triangle ABC.

AC22= AB22 + BC22

⟹ AC22 = 122 + 122

⟹ AC22 = 2

⟹ AC = 2–√2

Square Root of 2 on Number Line

Step IX: Now with AC as radius and C as the centre cut an arc on the same number line and name the point as D.

Step X: Since AC is the radius of the arc and hence, CD will also be the radius of the arc whose length is 2–√2.

Step XI: Hence, D is the representation of 2–√2 on the number line.

Represent Square Root of 2 on Number Line

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