This is the basic and conceptual question from real numbers chapter in which we have given a number (4-5√2) and we have to show that the given number is a irrational number
Kindly give me a detailed solution of this question
RS Aggarwal, Class 10, chapter 1D, question no 8
Let us assume that (4−5√2) is rational .
Subtract given number from 4, considering 4 is rational number. as we know difference of two rational numbers is rational.
4−(4−5√2)is rational
⇒5√2 is rational
which is only possible if 5 is rational and √2 is rational.
As we know prouduct of two rational number s rational
But the fact is √2 is an irrational.
Which is contradictory to our assumption.
Hence, 4−5√2 is irrational . hence proved.