Question

Prove that 5 + 3√2 is irrational?​

Answer 1

Answer:

Let us assume the contrary. That contradicts the fact that √2 is irrational. The contradiction is because of the incorrect assumption that (5 + 3√2) is rational. So, 5 + 3√2 is irrational.

Answer 2

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$\huge\sf\underline\red{Question}$

Prove that 5 + 3√2 is irrational.

$\huge\fbox\pink{˙❥answer}$

$assume \: \: that \: 5 + 3 \sqrt{2} is \: rational \: \\ \\ where \: \: a \: and \: \: b \: \: are \: integers \:$

$3 \sqrt{2} = \frac{a}{b} - 5 \\ \\ = 3 \sqrt{2} = \frac{a}{b} - \frac{5b}{b} \\ \\ = \sqrt{2} = \frac{a - 5b}{3b }$

NOW WE KNOW THAT A ,B ,3 AND 5 ARE INTEGERS. AND THEY ARE ALSO RATIONAL. (RHS are rational)

therefore, √2 IS RATIONAL , BUT WE KNOW THAT √2 IS IRRATIONAL.SO THERE IS A CONTRADICTION

$\small\orange{\textbf {\textsf {SO,5+3√2\:is\:an\:irrational\:number}}}$

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