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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