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Prove that the following number is irrational \((2+\sqrt{5})\)

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Prove that the following number is irrational \((2+\sqrt{5})\)
in Mathematics by ♦ Platinum (131,840 points) | 85 views

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\((2+\sqrt{5})\)
Let us assume that \((2+\sqrt{5})\)
is rational
Subtract given numbers from 2 , considering 2 is rational number as we know,difference of two rational numbers is rational.
\((2+\sqrt{5})\) is rational
but \(\sqrt{5}\) is irrational
Which is contradictory to our assumption.
So \((2+\sqrt{5})\) is an irrational.
by ♦ Platinum (131,840 points)

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