Show that:
(i) Negative of an irrational number is irrational.
(ii) The product of a non-zero rational number and an irrational number is an irrational number.
(i) Let the irrational number be √2.
Considering the negative of √2, we get -√2
We know that -√2 is an irrational number.
Hence, negative of an irrational number is irrational.
(ii) Let the non-zero rational number be 3.
Let the irrational number be √5.
Then, according to the question,
3 × √5 = 3√5 = 3 × 2.2 = 6.6, which is irrational.
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