Question

prove that √p+√q is irrational where p,q are primes

Answer 1

hey dear


here is your answer

Solution

Let √p + √q is rational number

A rational number can be writeen in the form of a/b

so

√p + √q = a/b

√p = a/b _ √q

√p = ( a - b √ q ) /b


P, Q are integers then ( a - b √Q ) /b

it is a rational number

So √p is also rational number


So it contradicts that √p + √Q is irrational number


So it is s false that it is irrational number


it is a rational number √p

hope it helps

thank you

Answer 2

Answer:

➡️ given numbers p , q

p , q are prime numbers

apply root on both numbers

√p , √q

Add this number = √p + √q

p is a prime number then √p is a irrational

q is a prime number √q is irrational

sum of two irrational numbers is an irrational.

√p + √q is an irrational numbers .

HENCE PROVED

Hope it helps

#Ravalika Rajula

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