Question

prove that root 5 + root 6 is irrational

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Answer 1

Explanation:

prove that root 5 + root 6 is irrational

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Answer 2

Answer:

let us assume that √5+√6 is rational.

$\sqrt{5 + \sqrt{6 \:} } \: is \: in \: the \: form \: of \: p \div q$

√5+√6=p/q

√6=p/q - √5

√6= p - √5q/q

squaring on both sides

6=(p -√5q)^2/q^2

substitute RHS

Finally we get RHS is irrational.

BUT LHS is rational

rational can't equal to irrational.

This contradicts that √5+√6 is irrational.

So, our assumption is wrong.

So,√5+√6 is an irrational.

I think so your doubt is cleared.

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