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Selina Solutions Class 9 Mathematics Solutions for Exercise 1(D) in Chapter 1 - Chapter 1- Rational and Irrational Numbers

Question 5 Exercise 1(D)

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.

Answer:

(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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