Question

Prove that
$\sqrt{p + \sqrt{q} }$
+ is an irrational, where p, q are primes.​

Answer 1

Answer:

Let us suppose that √(p + √q) is rational. 

Let √(p + √q) = a, where a is rational. 

=> √q = a – √p 

Squaring on both sides, we get 

q = a^2 + p - 2a√p

=> √p = (a^2 + p - q)/2a, which is a contradiction as the right hand side is rational number, while√p is irrational. 

Hence, √(p + √q) is irrational.

PLS MARK MY ANSWER AS BRAINLIEST IF IT HELPED U

I ONLY 8 MORE BRAINLIEST MARKS TO LEVEL UP

HELP ME PLS

:) THANK YOU

STAY HOME

STAY SAFE

Answer 2

Answer:

its simple, see down

Step-by-step explanation:

sq root of a prime no is always irrational.

Sum of 2 irrational nos is also irrational

Hence proved.