This question is taken from real numbers chapter in which we have given a number (2√3-1) and we have to show that the given number is a irrational number
Kindly solve the above problem in detail
RS Aggarwal, Class 10, chapter 1D, question no 7
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Let us assume that (2√3−1) is rational .
add 1 to be above number, considering 1 is rational number.
as we know , sum of two rational numbers is rational.
Sum = 2√3−1+1=2√3
which is only possible if 2 is rational and √3 is rational.
But the fact is √3 is an irrational number which contradicts to our assumption .
So, (2√3−1) is an irrational.