Question

plz answer these all questions​

Answer 1

Answer:

iii)

$6 + \sqrt{2} \\ let \: us \: assume \: to \: the \: contrary \: 6 + \sqrt{2} is \: rational \\ 6 + \sqrt{2} = \frac{a}{b} where \: a \: and \: b \: are \: co \: primes \: and \: b \: not \: = 0 \\ \sqrt{2 } = \frac{a}{b} - 6 \\ \sqrt{2} = \frac{a - 6b}{b}$

here LHS is irrational and RHS is rational. This contradicts a fact that √2 is irrational. This contradiction has arisen due to the incorrect assumption.

hence 6+√2 is irrational

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