Question

Prove that 3 root 5-2 root 3 is an irrational number

Answer 1

Hii friend!!
assume that 5-2 root 3 is rational
5-2 root 3 = a/b , where a and b are integers .
-2 root 3 = a/b - 5
2 root 3 = 5 - ab
2 root 3 = 5b/b - a/b
root 3 = 5b - a / 2b
we know that a, b , 2 and 5 are integers and they are also rational
therefore root 3 will be rational
but we know that root 3 is irrational
there is a contradiction
so, 5 - 2 root 3 is an irrational number

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