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CBSE Class 10 Answered

Prove that √p + √q is irrational,  where p,q are primes. 
Asked by rishijuneja2018 | 14 Apr, 2018, 08:51: PM
answered-by-expert Expert Answer

Solution 

Let √p + √q is rational number 

A rational number can be written 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  false that it is irrational number 


it is a rational number √p

hope it helps 

thank you ......

 

Answered by Arun | 15 Apr, 2018, 01:08: PM

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