Question

prove that 3 + 2√5 is irrational​

Answer 1

we know that root 5 is irrational

operation between rational /integers is always rational

therefore our assumption is wrong

3+2root 5 is irrational

Answer 2

$\huge\mathfrak\red{heya\:Mate}$

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✨ Let 3 + 2√5 is a rational no. then,it can be expressed in the form of

$\frac{p}{q}$

where p and q are co-prime and q not equal to 0.

✨Now, $\frac{p}{q}$ = 3 + 2√5

=> $\frac{p}{q}$ - 3 = 2√5

=> $\frac{p}{</em></strong><strong><em>2</em></strong><strong><em>q}$- 3 = √5

✨since, √ 5 is an irrational no.

there fore $\frac{p}{2q}$- 3 is also a irrational no. but it contradicts the fact that $\frac{p}{q}$- 3 is a rational no. hence 3 + 2√5 is an irrational no.

proved...