prove that √3-√2 is irrational number
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Suppose √3 - √2 is rational .
Let √3 - √2 = r where r is a rational.
∴ (√3 - √2)2 = r2
∴ 2 + 3 - 2√6 = r2
∴√6 = (5 - r2 ) / 2
Now , LHS = √6 is an irrational number .
RHS = (5 - r2 ) / 2 But rational number cannot be equal to an irrational.
∴our supposition is wrong.
∴ √3 - √2 is irrational .
Let √3 - √2 = r where r is a rational.
∴ (√3 - √2)2 = r2
∴ 2 + 3 - 2√6 = r2
∴√6 = (5 - r2 ) / 2
Now , LHS = √6 is an irrational number .
RHS = (5 - r2 ) / 2 But rational number cannot be equal to an irrational.
∴our supposition is wrong.
∴ √3 - √2 is irrational .
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