Question

Prove that (√3 - √2)3 is irrational

Solution

Sol : Suppose √3 - √2 is rational . Let √3 - √2 = r where r is a rational. ∴ (√3 - √2)^3 = r^3 ∴ (2 + 3 - 2√6)(√3 - √2) = r^3 5root3-2root18-5root2+2root12=r^3 Now , LHS is many terms with irrational numbers Because all the values inside the roots are not perfect roots RHS = r^3 But rational number cannot be equal to an irrational. ∴our supposition is wrong. ∴ √3 - √2 is irrational . Pls like if you are satisfied

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