Answer :
Assume that 2√3 - 1 is rational
2√3 = a/b , where a and b are integers .
⇒ 2√3 = a/b + 1
⇒ 2√3 = a/b + b/b
⇒ √3 = (a + b) / 2b
we know that a, b, and 2 are integers and they are also rational {i.e RHS is rational}
therefore √3 will be rational.
but we know that √3 is irrational.
there is a contradiction
so, 2√3 - 1 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 Expertsview all courses
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
RELATED QUESTIONS :
<span lang="EN-US
RS Aggarwal - Mathematics