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Question
Prove that (√3 - √2)3 is irrational
Prove that (√3 - √2)3 is irrational
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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
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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