Prove that 5-sqrt(3) is irrational given that sqrt(3) is irrational
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Let us assume the given number be rational and we will write the given number in p/q form
⇒5−
3
=
q
p
⇒
3
=
q
5q−p
We observe that LHS is irrational and RHS is rational, which is not possible.
This is contradiction.
Hence our assumption that given number is rational is false
⇒5−
3
is irrational
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