Q3 of 124 Page 1

Show that is an irrational numbers.

Let assume that is rational


Therefore it can be expressed in the form of , where p and q are integers and q≠0


Therefore we can write =


√3= 2 -


is a rational number as p and q are integers. This contradicts the fact that √3 is irrational, so our assumption is incorrect. Therefore is irrational.


More from this chapter

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1

Show that the following numbers are irrational.

(i) (ii)


(iii) 6 + (iv) 3 -

2

Prove that following numbers are irrationals:

(i) (ii)


(iii) (iv)

4

Show that is an irrational number.

 5

Prove that is an irrational number.