Question

Prove that 4-5root3 is an irrational no.

Answer 1

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Here is your solution....☺

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✴ Let ( 4 - 5√3 ) = a/b [ In a form of a rational number ]

=> 4 - 5√3 = a/b
=> 4 - a/b = 5√3
=> 4b - a / b = 5√3
=> 4b - a / 5b = √3

✴ Here, in LHS we have obtained a number i.e ; rational whereas in RHS we have √3 which is an irrational number.

Hence, Our assumption is wrong.....

✴ 4 - 5√3 is an irrational number.

Proved.....

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