Question

Show that 5√2 is an irrational number

Answer 1

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Answer 2

at first let us assume that 5√2 is rational. so, 5√2 can be written in the form of p/q, where p and q are co primes

5√2=p/q

=> √2 = p/5q

here, p,q and 5 are integers are integers so,. p/5q is rational
hence, √2 is also rational.
but it contradict the fact that √2 is irrational
hence we conclude that 5√2 is irrational

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