Question

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Answer 1

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.

$ac {}^{2} =ab {}^{2} + bc {}^{2}$

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$ac {}^{2} = 1 {}^{2} + 1 {}^{2}$

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$ac {}^{2} = 2$

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$ac = \sqrt{2}$

Square Root of 2 on Number Line

Hope it helps

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