Question

prove that 2root3 is irrational.....

Answer 1

we know that

$\sqrt{3} \: is \: a \: irrational \: number \:$

Let us assume that

$2 \sqrt{3 } \: is \: a \: rational \: number$

p/q = 2 root 3

$on \: rearranging \: the \:equation$

we get root 3 = p/2q

p q and 2 are integers so p / 2q is a rational number

so root3 is also a rational number but it contradict the fact that root 3 is an irrational number

this contradiction has arisen due to our wrong assumption .
so we conclude that 2 root 3 is a irrational


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Answer 2

similarly you can do the answer just exchange the digits

it would surely be correct

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