Question

Show That 7+√5 is an irrational number?​

Answer 1

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Answer 2

Answer:

Let 7 – √5 is a rational number. 7 + √5 = a/b, b ≠ 0 …(i) Where a and b co-prime integer number. Equation (i) can be written as √5 = a/b – 7 or √5 = (a - 7b)/b ….(ii) Since, a and b are integers. So (a - 7b)/b will be rational number, so from equation (ii) we find that √5 is a rational number. But we know that √5 is a irrational number. So this result is contradicted. So our hypothesis is wrong. Hence 7 + √5 is a rational number.Read more on Sarthaks.com - https://www.sarthaks.com/748048/prove-that-7-5-is-an-irrationalnumber