Question

Prove that 13+25✓2 is irrational

Answer 1

Hey !

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prove 13 + 25√2 is irrational.

Let us consider in contradiction that 13 + 25√2 is rational.

let us assume 13+25√2 = a / b

25√2 = a/ b - 13

√2 = a/b -13/25

√2 = 25a - 13b / 25 b

√2 = 25 ( integer ) - 13 ( integer ) / 25 ( integer )

{ integer / integer = p/q }

we know that a number in the form of p/q is rational.

So , 13+25√2 is rational.

But we know that √2 is irrational .

Hence our assumption is wrong.

So , 13+25√2 is irrational

Hence , proved .

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Answer 2

Hey friend!!

Here's ur answer...

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$let \: 13 + 25 \sqrt{2} \: be \: a \: rational \: number. \\ \\ so \: \: 13 + 25 \sqrt{2} = \frac{a}{b} \: where \: a \: and \: b \: are \: co \: primes. \\ \\ 25\sqrt{2} = \frac{a}{b} - 13 \\ \\ 25 \sqrt{2} = \frac{a - 13b}{b} \\ \\ \sqrt{2 } = \frac{a - 13b}{25b} \\ \\ but \: \sqrt{2} \: is \: irrational \: \\ so \: by \: contradiction \: \\ \\ 13 + 25 \sqrt{2} \: is \: also \: irrational \: . \\ \\ hence \: proved........$
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