Question

please solve this question ​

Answer 1

Step-by-step explanation:

Solution:

Yes, ‘ab’ is necessarily an irrational.

For example, let a = 2 (a rational number) and b = √2 (an irrational number)

If possible let ab = 2√2 is a rational number.

Now, aba = 22√2 = √2 is a rational number.

[∵ The quotient of two non-zero rational number is a rational]

But this contradicts the fact that √2 is an irrational number.

Thus, our supposition is wrong.

Hence, ab is an irrational number.

Solution:

Yes, x + y is necessarily an irrational number.

For example, let x = 3 (a rational number) and y = √5 (an irrational number)

If possible let x + y = 3 + √5 be a rational number.

Consider pq = 3 + √5, where p, q ∈ Z and q ≠ 0.

Squaring both sides, we have

Number Systems Class 9 Extra Questions Maths Chapter 1 with Solutions Answers 6

∵ pq is a rational

⇒ √5 is a rational

But this contradicts the fact that √5 is an irrational number.

Thus, our supposition is wrong.

Hence, x + y is an irrational number.