Question

prove that 3 + 2√5 is irrational

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Answer 1

this is your perfect time so please take it I think I help you

Answer 2

here is ur answer:

Let 3 + 2√5 be a rational no.

so, it can be written in a form of p/q

$\frac{p}{q} = 3 + 2 \sqrt{5} \\ \\ \frac{p}{q} - 3 = 2 \sqrt{5} \\ \\ \frac{p - 3q}{q} = 2 \sqrt{5} \\ \\ \frac{p - 3q}{2q} = \sqrt{5}$

since √5 is an irrational no. so, it can't be equal to p-3q/2q as it's rational no. Hence our assumption is wrong, 3 + 2√5 is an irrational no.

Hence proved.

hope it helps you ❤