Question

Show that 5/root 2 is an irrational number assuming root 2 to be an irrational number

Answer 1

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Answer 2

Step-by-step explanation:

Let  $5/\sqrt{2}$ be a rational number.

So, $5/\sqrt{2}$ = a / b where a and b are co-prime. and b $\neq$ 0

$\sqrt{2}$a = 5b

$\sqrt{2}$ = 5b / a

5b / a is a rational number. So, $\sqrt{2}$ should also be a rational number.

But as proved $\sqrt{2}$ is an irrational number.

Therefore, our assumption is wrong.

Therfore,  $5/\sqrt{2}$ is an irrational number.

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