One of the most important and conceptual question from real numbers in which we have given a number (2-3√5) and it was already asked in previous year papers 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 3(viii)
Let us assume that (2−3√5) is rational.
subtract given numbers from 2 , considering 2 is rational number.
as we know , difference of two rational numbers is rational
2−(2−3√5)is rational.
⇒3√5 is rational
above result is possible if 3 is rational and √5 is rational.
Because , product of two rational numbers is rational.
but the fact is √5 is an irrational .
Our assumption is wrong, and (2−3√5) is irrational