Question

5-✓3is irrational number​

Answer 1

Yes, given number is irrational number.

Answer 2

let us suppose that

$5 - \sqrt{3}$

is rational then it can be written as In the form of

$\frac{a}{b}$

where a and b (b is not equal to 0) are co-prime.

hence

$5 - \sqrt{3 } = \frac{a}{b} \\ - \sqrt{3} = \frac{a}{b} - 5 \\ - \sqrt{3} = \frac{a - 5b}{b} \\ \sqrt{3} = - \binom{a - 5b}{b} \\ \sqrt{3} = \frac{5b - a}{b} \\ here \: - \frac{a - 5b}{b} \: is \: rational \: \\ but \: \sqrt{3} is \: irrational \: this \: is \: contradiction \\ hence \: our \: assumption \: is \: incorrect \:$

the number is irrational

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