Question

Prove tha √p+√q is irrational​

Answer 1

Step-by-step explanation:

Suppose that √p + √q is rational ,say r

Then ,√p + √q = r ( note that r is not equal to 0 ).

√q =r - √p

(√q)2 = ( r - √p)2

q = r2 + p - 2r√p

2r√p = r2 + p - q

√p = r2 + p - q / 2r

As r is rational and r is not equal to 0 ,so r2 + p - q /2r is rational

= √p is rational .

But this contradicts that √p is irrational

Hence , our supposition is wrong .

Therefore , √p + √q is an irrational number.

Answer 2

Answer:

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