Question

4. Prove that 3 + 2 V5 is irrational.
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Answer 1

$\boxed{solution\:by\:bhaswati7}$

Answer 2

$\huge\underline\mathfrak{Solution :}$

let's suppose that 3+2√5 is a rational no.

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

( where q≠ 0 )

$2 \sqrt{5 } = ( \frac{p }{q} - 3) \\ \\ \sqrt{5 } = \frac{1}{2} ( \frac{p}{q} - 5)$

= √3 is a rational no .

= LHS ≠ RHS

• So our Assumption is wrong

= 3+2√5 is a irrational no.