# Prove that of the Numbers 2 + Sqrt (5) is Irrational: - Mathematics

Prove that of the numbers  2 + sqrt (5) is irrational:

#### Solution

Let   2 + sqrt (5)  be rational.
Hence,   2 + sqrt (5) and sqrt( 5 ) are rational.
∴  (2 + sqrt (5)) – 2 =  2 + sqrt (5)–  2 = sqrt (5) = rational [∵Difference of two rational is rational]
This contradicts the fact that sqrt (5) is irrational.
The contradiction arises by assuming   2 - sqrt (5) is rational.
Hence,  2 - sqrt (5)  is irrational.

Concept: Concept of Irrational Numbers
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