Question

prove that 5√2 is not a rational number

Answer 1

Hey ....

To prove :- 5√2 is an irrational no.

we know that √2 is an irrational no.

let's, 5√2 is a rational no
5√2+1/5=√2------(I)

{rational ×rational =rational}

A/Q to eq. 1 √2 Is a rational no. bt we know that √2 is an irrational no. so.... our contradiction was wrong and.....

5√2 Is an irrational no.......

Here is ur answer in this figure...

Hope this will help u...

Answer 2

HOLA

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Let us assume 5√2 as rational

$5 \sqrt{ {2}^{} } = \: \frac{a}{b} \\ \\ square \: on \: both \: sides \\ \\ (5 \sqrt{2} ) {}^{2} =( \: \frac{a}{b} ) {}^{2} \\ \\ 2 \: = \: \frac{a \: - 25}{b}$
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Hence , A and B are divisible by 5√2

Hence , our assumption was wrong 5√2 is irrational