Show that 4+√5 is an irratinal number
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Let us assume that (4−52) is rational .
Subtract given number from 4, considering 4 is rational number. as we know difference of two rational numbers is rational.
4−(4−52)is rational
⇒52 is rational
which is only possible if 5 is rational and 2 is rational.
As we know prouduct of two rational number s rational
But the fact is 2 is an irrational.
Which is contradictory to our assumption.
Hence, 4−52 is irrational . hence proved.
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