My Cart
Your Cart 0

    Your cart is empty.

  • Total (Amount) ₹0.00
NCERT Exemplar · Class 9 · Maths

Chapter 1: Number Systems

Practice each question, then open the answer or worked solution.

Read chapter PDFDownload PDF

Exercise 1.2

Textbook page 6 · 2 questions
Q1Written answer

Let x and y be rational and irrational numbers, respectively. Is x + y necessarily an irrational number? Give an example in support of your answer.

Show solutionHide solution
Worked solution

Yes, if x and y are rational and irrational numbers, respectively, then x+ y is an irrational number.

For example,

Let x = 5 and y = √2.

Then, x+y = 5 + √2 = 5 + 1.414… = 6.414…

Here, 6.414 is a non-terminating and non-recurring decimal and therefore is an irrational number.

Hence, x + y is an irrational number.

Q2Written answer

Let x be rational and y be irrational. Is xy necessarily irrational? Justify your answer with an example.

Show solutionHide solution
Worked solution

No, if x is a rational number and y is an irrational number, then xy is not necessarily an irrational number. It can be rational if x = 0, which is a rational number.

For example:

Let y = √2, which is irrational.

Consider x = 2, which is rational.

Then, x × y = 2 × √2 = 2√2, which is irrational.

Consider x = 0, which is rational.

Then xy = 0 × √2 = 0, which is rational.

Therefore, we can conclude that the product of a rational and an irrational number is always irrational, only if the rational number is not zero.