Question

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SHOW THAT 3+2√7 IS IRRATIONAL


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Answer 1

Given to prove :-

3 + 2√7 is an irrational number

Prove :-

Let us assume that 3 + 2√7 is an rational number and p/q be the form of integer where the integer are positive and their HCF is 1

3 + 2√7 = p/q

2√7 = p/q - 3

2√7 = p - 3q/q

√7 = p - 3q/2q

Hence, RHS is represented as p/q form but √7 is an irrational number. Therefore, our assumption is wrong and 3 + 2√7 is an irrational number

Hence prove