State true or false: Product of a rational and an irrational number is always irrational.

see full answer

Start JEE / NEET / Foundation preparation at rupees 99/day !!

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

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

A statement says that the product of a rational number and an irrational number is a rational number, and we have to state if it’s true or not.
Now, we know that any operation, be it addition, subtraction, multiplication and division, performed between a rational number and an irrational number gives the result as an irrational number.
But, if we take the product of a rational number say 0 with an irrational number say

2

, the product will be

0 × 2 = 0

.
This contradicts the given statement as 0 is rational number.
Hence, the statement is false.
Product of a rational and an irrational number is only irrational when not multiplied by 0.
So, the correct option is 2.

Watch 3-min video & get full concept clarity

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

🔥 Start Your JEE/NEET Prep at Just ₹1999 / month - Limited Offer! Check Now!

Get Expert Academic Guidance – Connect with a Counselor Today!

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