Question

Prove that 5-✓2 is irrational.​

Answer 1

QUESTION :-

Prove that 5 - √2 is irrational.

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SOLUTION :-

Let us consider the number as a rational number, so it can be written as p/q form.

$= > 5 - \sqrt{2} = \frac{p}{q} \\ \\ = > - \sqrt{2} = \frac{p}{q} - 5 \\ \\ = > - \sqrt{2} = \frac{p - 5q}{q} \\ \\ = > - \sqrt{2} \times - 1 = \frac{p - 5q}{q} \times - 1 \\ \\ = > \sqrt{2} = \frac{ - p + 5q}{q}$

Here, -p+5q/q is rational number because it is in the form of rational number, but we know that √2 is not a rational number. so,

$\sqrt{2} \neq \frac{ - p + 5q}{q}$

Our consideration was wrong and 5 - √2 is an irrational number.

hope it helps.

#BeBrainly :-)