Q7 of 23 Page 1

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


Let 3√3be a rational number say r.
Then 3√3=r
We know that LHS(√3) is an irrational number therefore RHS should also be an irrational number.

Thus r is an irrational number.

Therefore, our assumption that 3√3 is a rational number is wrong.

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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. 6

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

2  +  √2 is not a rational number.

8

Show that is not arational number.

9

Identify the following as rational or irrational numbers. Give the decimalrepresentation of rational numbers.
(i)√4
(ii) 3√18
(iii)√1.44
(iv)
(v) -√0.64
(vi) √100