Question

Prove that 7+root5 is irrational

Answer 1

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.