State True/False.

The product of two irrational numbers is an irrational number.

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

True

False

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

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.

Result Producing online coaching for JEE/NEET of south India

Largest All India Test Series for JEE/NEET

Best Books for IIT JEE

Best Books for NEET

How to Join IIT after 10th