Question

pla
$prove \: \: that \: 3 + 2 \sqrt{2 \: is \: irrational \: number}$
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Answer 1

To prove:-

3+2√2 is irrational

Proof:-

Let 3+2√2 be rational

i.e,3+2√2=$\frac{a}{b}$ [where a and b are co-prime integers and a&b are not equal to zero(a&b≠0)]

→3+2√2=$\frac{a}{b}$

→2√2=$\frac{a}{b}$+3 [°•°Cross multiply]

→2√2=$\frac{a+3b}{b}$

→√2=$\frac{a+3b}{2b}$

→As √2 is irrational and $\frac{a+3b}{2b}$ is rational, It contradicts the fact IRRATIONAL≠RATIONAL.

=>LHS≠RHS

•THUS, 3+2√2 is ir-rational.

$\rule{200}{1}$