# The product of any two irrational numbers is

a. always an irrational number

b. always a rational number

c. always an integer

d. sometimes rational, sometimes irrational

**Solution:**

We know that

A number which cannot be expressed in the form p/q where p and q are __integers__ and q ≠ 0 is called an __irrational number__.

The product of two irrational numbers can be rational or irrational based on the numbers

Example - √2 × √2 is 2 which is a __rational number__

Similarly

√2 × √3 is √6 which is irrational

Therefore, the product of any two irrational numbers is sometimes rational, sometimes irrational.

**✦ Try This: **What is the product of 5√2 and 3√2?

We have to find the product of 5√2 and 3√2

5√2 × 3√2 = 15 × 2

= 30

Therefore, the product is 30.

**☛ Also Check: **NCERT Solutions for Class 9 Maths Chapter 1

**NCERT Exemplar Class 9 Maths Exercise 1.1 Problem 4**

## The product of any two irrational numbers is a.always an irrational number, b. always a rational number, c. always an integer, d. Sometimes rational, sometimes irrational

**Summary**:

The product of any two irrational numbers is sometimes rational, sometimes irrational. This is because √2 × √2 is 2 which is rational whereas √2 × √3 is √6 which is irrational

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