Question

The product of two irrational numbers is an irrational number (True/False).

Answer 1

SOLUTION :  

This statement the product of two irrational numbers is an irrational number is FALSE.  

★★ Because  the product of two irrational numbers is not always  an irrational number it is sometimes a  rational number .

For e.g :  

★ Let the 2 irrational numbers be √2 & √5

Product of  √2 & √5 = √10

√10 is an IRRATIONAL NUMBER.

★ Let the 2 irrational numbers be √2 & √18 .

Product of √2 & √18 = √36 = 6  

6 is a RATIONAL NUMBER .

Hence,the product of two irrational numbers is sometimes rational number and sometimes an irrational number is FALSE.

★★RATIONAL NUMBERS : A number that can be expressed in the form p/q,  where p and q are integers and q ≠ 0 is called rational number.

★★IRRATIONAL NUMBERS :  

A number that cannot be expressed in the form p/q,  where p and q are integers and q ≠ 0 is called irrational number.

HOPE THIS ANSWER WILL HELP YOU…..

Answer 2

Answer:

The statement is false. Product of two irrational numbers is not always an irrational number.

Step-by-step explanation:

(i)

Let us consider the two irrational numbers as (7 + √5) and (7 - √5)

We know that (a + b)(a - b) = a² - b²

⇒ (7)² - (√5)²

⇒ 49 - 25

⇒ 24.

Rational number.

(ii)

Let us consider the two irrational numbers as √3 and √8.

⇒ √3 * √8

⇒ √24.

Irrational number.

Hope it helps!