Given that/ 2irrational prove that 5+3/2 is an irrational no
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Suppose 5 +3√3 is rational .
Let 5 +3√3 = r where r is a rational.
∴ (5 +3√3)2 = r2
∴ 25+27 +30√3 = r2
∴√3 = (r2 - 52) / 30
Now , LHS = √3 is an irrational number .
RHS (r2 - 7) / 2 is a rational number .
But rational number cannot be equal to an irrational.
∴our supposition is wrong.
∴ 5 + 3√3 is irrational
Suppose 5 +3√3 is rational .
Let 5 +3√3 = r where r is a rational.
∴ (5 +3√3)2 = r2
∴ 25+27 +30√3 = r2
∴√3 = (r2 - 52) / 30
Now , LHS = √3 is an irrational number .
RHS (r2 - 7) / 2 is a rational number .
But rational number cannot be equal to an irrational.
∴our supposition is wrong.
∴ 5 + 3√3 is irrational
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