Question

Giventhat undrootw irrational,prove that(5+3underroot2)isan irattional no

Answer 1

√2 is a irrational number.
let 5+3√2 is rational no. say r
5+3√2=r
Now √2=r-5/3
here √2
is irrational number so this is also irrational.
our supposition is wrong
it is irrational number

Answer 2

hello friend,
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$let \: 5 + 3 \sqrt{2} \: be \: a \: rational \: number \: \\ hence \: 5 + 3 \sqrt{2} = \frac{a}{b} \: \: \: \: \: (where \: a \: and \: b \: are \: two \: co \: \\ prime \: integers) \\ 3 \sqrt{2} = \frac{a}{b} - 5 \\ 3 \sqrt{2} = \frac{a - 5b}{b } \: \: \\ \sqrt{2} = \frac{ a - 5b }{3b} \\ but \: we \: know \: that \: \sqrt{2} is \: irrational \: number \: \\ this \: contadiction \: is \: a \: fact \\ hence \: 5 + 3 \sqrt{2} is \: irrational \: number$
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I hope it will help :-)