Question

Assuming that V2 is irrational, show that 5V2 is an irrational number​

Answer 1

Assuming that V2 is irrational, show that 5V2 is an irrational number

let us assume that 5+\sqrt{2}

2

is a rational number

5+\sqrt{2}

2

=p/q

\sqrt{2}

2

=p/q-5 (rational-rational=rational)

therefore p/q-5 is rational then \sqrt{2}

2

is also rational

but it is given that \sqrt{2}

2

is irrational in the question

so, it is contradiction to our assumption

then 5+\sqrt{2}

2

is irrational.

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