Question

a prove that
5√q is an irrational number​

Answer 1

$\huge \underline \mathfrak{ \red{answer}}$

$let \: \sqrt{5} \: is \: a \: rational \: number \\ in \: form \: of \frac{p}{q} \: where \: q \: not \:e qua l \: to \\ zero \\ \sqrt{5} = \frac{p}{q} \\ \sqrt{5} \times q = p \\ squaring \: on \: both \: side \\ {5p}^{2} = {p}^{2} (equation(1)) \\ {p}^{2} is \: divisible \: ny \: 5. \\ p \: is \: divisible \: by \: 5 \\ put \: {p}^{2} \: in \: equation(1) \\ 5 {q}^{2} = 25 {d}^{2} \\ {q}^{2} = 5 {d}^{2} \\ so \: q \: is \: divisible \: by \: 5$

➡ Thus p and q have a common factor of 5.

$therefore \: \sqrt{5 } \: is \: a \: irrational \: no.$

Step-by-step explanation:

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