Question

hi guys... please solve this question.
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Answer 1

Step-by-step explanation:

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.

Solution:

Number Systems Class 9 Extra Questions Maths Chapter 1 with Solutions Answers 7

Number Systems Class 9 Extra Questions Maths Chapter 1 with Solutions Answers 8

On the number line, take OA = 1 unit. Draw AB = 1 unit perpendicular to OA. Join OB.

Again, on OB, draw BC = 1 unit perpendicular to OB. Join OC.

By Pythagoras Theorem, we obtain OC = √3. Using

compasses, with centre O and radius OC, draw an arc, which intersects the number line at point

D. Thus, OD = √3 and D corresponds to √3.