Question

show that √p-√q as irrational
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Answer 1

Step-by-step explanation:

To prove : p+q is irrational 

Proof :

We will proof by the method of contradiction,

Let's assume

p+q is rational, where p & q are distinct primes

i.e. p+q=k, where k is rational 

Rational numbers are closed under multiplication, So if we square both sides, we should still get rational number on both sides

(p+q)2=k2

⇒p+q+2pq=k2

⇒2pq=k2−p−q

⇒pq=21(k2−p−q)

Now, k2,p,q & 2 are all rational, and rational number being closed under subtraction and division, (k2−p−q)/2 will be rational.

But as p & q are both primes, then pq is not a perfect square and there by pq is not rational. Hence , we reach a contradiction. Therefore, our original assumption must be wrong.

So, p+q is irrational, where p & q are distinct primes.

Answer 2

Answer:

the numbers which are not able to form in p/q they are call irrational number .

and now .

√p is irrational because there is no q form right .

similarly √ q is also a irrational number

Step-by-step explanation:

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