Question

prove 3√5 is a irrational number​

Answer 1

Answer:

let 3 root 5 be a rational number

so

$3 \sqrt{5} = \frac{p}{q} \\ that \: means \: it \: can \: be \: written \: a \\ \sqrt{5 } = \frac{p}{3q} \\ which \: is \: also \: a \: rational \: number$

but we clearly know that

$\sqrt{5} \: is \:irrational$

this contradicts the fact that 3 root five is rational

hence it is irrational

proved

Answer 2

let if possible 3root 5 is irrational 3 root 5 = a / b , b not equal to 0

root 5 = a/3b

》Since , a and b are integers

a/3b is irrational

root 5 is irrational

But this contradicts the fact that root 5 is irrational

therefore , Our assumption is wrong

therefore , 3root5 is irrational

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