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