State True/False.

The product of two irrational numbers is an irrational number.

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True

False

answer is B.

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Detailed Solution

Given to find the product of two irrational numbers is an irrational number or not.
Rational numbers are those that can be represented as p/q where p, q are integers and q is not equal to zero.
A real number that cannot be expressed as a ratio of integers is an irrational number.
An irrational number's decimal expansion is neither terminating nor recurring.
Let

(p + q) and (p − q)

be two irrational numbers, with both p and q are rationals and q is not a perfect square.
Multiply the irrational numbers,
Question Image

Given p is a rational number, and thus

p 2

is also a rational number.
Therefore the product of two irrational numbers is not always an irrational number.
Thus the statement, product of two irrational numbers is an irrational number is false.
Hence the correct option is 2.

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