let us assume that 3 + 2√5 is rational.
3 + 2√5=a/b( a and b are Co prime)
2√5 =a-3b/b
√5(irrational)=a-3b/2b
we know that √5 is irrational.
therefore rational number is not equal to irrational number.
Our assumption is incorrect that 3 + 2√5 is rational
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let us assume that 3 + 2√5 is rational.
3 + 2√5=a/b( a and b are Co prime)
2√5 =a-3b/b
√5(irrational)=a-3b/2b
we know that √5 is irrational.
therefore rational number is not equal to irrational number.
Our assumption is incorrect that 3 + 2√5 is rational