Q13 of 51 Page 1

Prove that is an irrational number.

If possible, let be a rational number equal to x. Then,

x =


x2 = ()2


= ()2 + ()2 + 2 * *


= 3 + 5 + 2


= 8 + 2


x2 – 8 = 2


=


Now, x is rational


x2 is rational


is rational


is rational


But, is irrational


Thus, we arrive at a contradiction. So, our supposition that + is rational is wrong.


Hence, + is an irrational number.


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Complete the following sentences:

(i) Every point on the number line corresponds to a ….number which many be either …… or ……


(ii) The decimal from of an irrational number is neither……. nor…..


(iii) The decimal representation of a rational number is either ……… or ……….


(iv) Every real number is either …………… number or ……………. number.