Math, asked by nitishbavalattoxpvrm, 1 year ago

Prove that root 2 plus root 5 whole square is irrational

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Answered by mastermind10009

hope you like this answer

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Answered by Mylo2145

Lets assume to the contrary that
$2 + \sqrt{5}$
Is a rational no.
Then there must be co prime a and b such that
$2 + \sqrt{5 } = \frac{a}{b}$
$= \sqrt{5 } = \frac{a}{b } - 2$
$= \sqrt{5} = \frac{a - 2}{b}$
Here; a, b, and -2 are integers...thus
$\frac{a - 2}{b}$
Is rational

Mylo2145: thus root 5 should be rational

Mylo2145: ut this contradicts the fact that root 5 is irrational

Mylo2145: this contradiction has arisen due to our incorrect assumption that 2+root5 is rational.

Mylo2145: therefore 2+root5 is rational

Mylo2145: hope it helps u

Mylo2145: mark as brainliest

nitishbavalattoxpvrm: See question carefully

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