Question

show that it is an irrational number​

Answer 1

Assume $\sqrt7-\sqrt5$ is rational, to reach the contradiction.

Let  $x=\sqrt7-\sqrt5$  where $x$ is rational.

$\!\implies\ x^2=(\sqrt7-\sqrt5)^2\\\\\implies\ x^2=12-2\sqrt{35}\\\\\implies\ \dfrac{12-x^2}{2}=\sqrt{35}$

Here the LHS is rational while the RHS is irrational.

Hence we get our assumption contradicted!

Answer 2

Answer:

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