Q2 of 18 Page 14

Prove that is irrational.

Let is rational.


Therefore,


We can find two integers p & q where, (q ≠ 0) such that




Since p and q are integers, will also be rational and therefore, is rational.


This contradicts the fact that is irrational.


Therefore, is irrational.


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Prove that is irrational.

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Prove that the following are irrationals:

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(ii)


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Without actually performing the long division, state whether the following rational numbers will have a terminating decimal expansion or a non-terminating repeating decimal expansion:





















(i)



(ii)



(iii)



(iv)



(v)



(vi)



(vii)



(viii)



(ix)



(x)