Question

Prove that √5 + √7 is an irrational number

Answer 1

ANSWER:-

Let √5+√7 is an rational number and it is in the form of p/q form (where p and q are co primes)

• √5+√7=p/q

SQUARING ON BOTH SIDES..

• (√5+√7)²= (p/q)²
• (√5)²+(√7)²+2(√5)(√7)=p²/q²
• 5+7+2√35=p²/q²
• 12+2√35=p²/q²
• 2√35=p²-12/q²
• √35=p²-12/q²/2

√35 is a irrational

p²-12/q²/2 is rational

and, rational is not equal to irrational

it is contradiction due to our wrong assumption that √5+√7 is rational...

SO, √5+√7 is irrational Number.....

HOPE THE ANSWER HELPS YOU........