Prove that 7+root5 is irrational

1.	Prove that 7+root5 is irrational
Answer» SOLUTION : °•° Let Assume 7 + √5 is rational number. Rational Number have some condition. b ≠ 0. HCF ( a , b ) = 1. A/Q, $\tt : \implies 7 + \sqrt{5} = \dfrac{a}{b}$ $\tt : \implies \sqrt{5} = \dfrac{a}{b} - 7$ $\tt : \implies \sqrt{5} = \dfrac{a - 7b}{b}$ ★ Here, We are notice √5 is irrational number and a - 7b /b is rational number. $\tt \dagger \: \: \: \: \: Irrational \neq Rational \: number.$ So, Our assumption was wrong 7 + √5 is not rational number it's irrational number. Hence Proved. Some More QUESTIONS : prove that √p + √q is irrational number. prove that √p is irrational number. prove that √5 + √7 is irrational number. prove that 2√5 + 4 is irrational number.

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