Question

$5 \sqrt{3 \: is \: irrational}$
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Answer 1

Given

$5 \sqrt{3}$

let this number be a rational number thus

$5 \sqrt{3} = \frac{p}{q} \\ where \: (p \: and \: q) \: belongs \: to \: inegers \: \\ and \: hcf(p \: and \: q) = 1$

Thus

$\sqrt{3} = \frac{p}{5q}$

• p/5q would be rational
• but it is equal to an irrational number.
• Thus our assumption is wrong and 5√3 is an irrational number.

#answerwithquality

#BAL