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