Question

Show that 3+2root2 is irrational

Answer 1

QUESTION :-

Show that 3 + 2√2 is irrational.

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SOLUTION :-

Let us consider 3 + 2√2 as a rational number, so it can be written in p/q form.

$= > 3 + 2 \sqrt{2} = \frac{p}{q} \\ \\ = > 2 \sqrt{2} = \frac{p}{q} - 3 \\ \\ = 2 \sqrt{2} = \frac{p - 3q}{q} \\ \\ = > \sqrt{2} = \frac{p - 3q}{q} \div 2 \\ \\ = > \sqrt{2} = \frac{p - 3q}{q} \times \frac{1}{2} \\ \\ = > \sqrt{2} = \frac{p - 3q}{2q}$

Here,

p-3q/2q is rational but we know that √2 is an irrational number. so,

$\sqrt{2} \neq \frac{p - 3q}{2q}$

And also our consideration was wrong, so that 3 + 2√2 is irrational.

hope it helps.

#BeBrainly :-)