Q. 84.2( 41 Votes )

# Prove that

Answer :

5√2 is an irrational number and subtraction of a rational number and an irrational number is an irrational number.

, 4 - 5√2 is irrational, where 5√2 is an irrational number while 4 is a rational number.

Alternative - Assume that 4 - 52 is rational
4 - 52 = a/b , where a and b are integers .
- 52 = a/b - 4
5√2 = 4 - a/b
5√2 = 4b/b - a/b
2 = (4b – a) / 5b
we know that a, b, 4 and 5 are integers and they are also rational {i.e RHS is rational}
therefore2 will be rational.
but we know that2 is irrational.
there is a contradiction
so, 4 - 52 is an irrational number

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

<span lang="EN-USRS Aggarwal - Mathematics