CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Prove that 4-3 is an irrational number, given that 3 is an irrational number.


Solution

Let us assume that 4-3 is a rational number.

Thus, 4-3 can be represented in the form of pq, where p and q are integers, q ≠ 0, p and q are co-prime numbers.

4-3=pq-3=pq-4-3=p-4qq3=4q-pqSince, 4q-pq is rational3 is rationalBut, it is given that 3 is an irrational number.Therefore, our assumption is wrong.Hence, 4-3 is an irrational number. 

Mathematics
RS Aggarwal (2019)
All

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
Same exercise questions
View More


similar_icon
People also searched for
View More



footer-image