Prove that 5-2/7root3 is an irrational number
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Let, 5-2/7√3 be rational.
Thus, 5-2/7√3=p/q
=> 1/7√3=p/(5-2)q
=> 1/√3=7p/(5-2)q
=> √3 = (5-2)q/7p
(5-2)q/7p is rational as 5,2,7,p and q are integers.
But, √3 as we know is irrational. Thus our assumption is wrong.
Thus, 5-2/7√3 is irrational. [PROVED]
Thus, 5-2/7√3=p/q
=> 1/7√3=p/(5-2)q
=> 1/√3=7p/(5-2)q
=> √3 = (5-2)q/7p
(5-2)q/7p is rational as 5,2,7,p and q are integers.
But, √3 as we know is irrational. Thus our assumption is wrong.
Thus, 5-2/7√3 is irrational. [PROVED]
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