One of the most important and conceptual question from real numbers chapter as it was already asked in various important examinations in which we have given a number 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 10

## Let us assume that 5√2is a rational.

Which is only possible if 5 is rational and √2 is rational.

as we know product of two rational number is rational.

But the fact is √2 is an irrational.

which contradicts our assumption .

5√2 is an irrational hence proved.