Question

prove that 2 + 7√2 is an irrational number​

Answer 1

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Let us assume that 2+7√2 is rational,

so,

$2 + 7 \sqrt{2} = \frac{a }{b}$

where a and b are co prime

$7 \sqrt{2} = \frac{a - 2b}{b} \\ \\ \sqrt{2} = \frac{a - 2b}{7b}$

we know that √2is rational but it is shown in the form of

$\frac{p}{q}$

so, this contradiction is arissen because of our wrong assumption,

so,

2+7√2 is irrational

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hops this may help you

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