Q6 of 23 Page 1

You have seen that √2 is not a rational number. Show that

2  +  √2 is not a rational number.


Let 2  +  √2be a rational number say r.
Then,2  +  √2=r
√2=r-2
But, √2is an irrational number.

LHS is irrational thus RHS should also be irrational to maintain the equality.


Therefore, r – 2 is also an irrational number
⇒ r is an irrational number.
Hence our assumption r is a rational number is wrong.
Hence, 2  +  √2 is not a rational number.

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4

Complete the following:
(i) Every point on the number line corresponds to a _____________  numberwhich may be either  _____________ or _____________.
(ii) The decimal form of an irrational number is neither _____________  or_____________.
(iii) The decimal representation of the rational number https://gs-post-images.s3.amazonaws.com/user_files/63094/15039/images/extra-1_files/Image3058.gif is _____________.
(iv) 0 is  _____________  number. [Hint: a rational /an irrational]

5
Which of the following rational numbers have the terminating decimalrepresentation?
(i)3/5             (ii)7/20                   (iii)2/13
(iv) 27/40        (v)133/125            (vi)23/7
[Making use of the result that a rational number p/q where p and q have nocommon factor(s) will have a terminating representation if and only if theprime factors of q are 2's or 5's or both. 7

Prove that
Prove that3√3is not a rational number.

8

Show that is not arational number.