Question

show that root 5 and root 7 is an irrational number​

Answer 1

Answer:

Step-by-step explanation:

Let assume √5+√7 is a rational number .

Rational Number = $\frac{p}{q}$, where p, q is integer.

√5+√7=$\frac{p}{q}$

Squaring both sides,

(√5+√7)²=($\frac{p}{q}$)²

√5²+√7²+2(√5)(√7)=($\frac{p}{q}$)²

5+7+2(√35)=($\frac{p}{q}$)²

2√35=($\frac{p}{q}$)²-12

√35=p²-12q²/2q

p, q are integers then(p²-12q²)/2q is a rational number'

Then √35 is a rational number.

But it contradicts the fact that√35 is a irrational number.

Our assumption is incorrect.

√5+√7 is an irrational number.