Question

prove that root5 + 7 root2 are irrational ? how ?

Answer 1

let √5+7√2 be a rational no

√5+7√2 = b/q

√5 = b/q -7√2

since we considers 7√2 a rational no

√5 is a rational no

but √5 is a irrational no therefore our assumptions is wrong

thus √5+7√2 is a irrational no

Answer 2

To Prove :

5 + 7√2 is Irrational number.

Solution :

°•° Let assume 5 + 7√2 is rational number.

So,

$\tt : \implies 5 + 7 \sqrt{2} = \dfrac{a}{b}$

Where as a and b are Co prime and HCF( a , b ) = 1.

$\tt : \implies 7 \sqrt{2} = \dfrac{a}{b} - 5$

$\tt : \implies 7 \sqrt{2} = \dfrac{a - 5b}{b}$

$\tt : \implies\sqrt{2} = \dfrac{a - 5b}{7b}$

We know, √2 is irrational number and a - 5b /7b is rational number.

$\tt {Irrational \red{\neq }Rational}$

So, Our assumption was wrote 5 + 7√2 is Irrational number.

Hence Proved.