Question

Sum of a rational and irrational numbers are always an irrational number.

Answer 1

heya......



Let rational number + irrational number = rational number


And we know " rational number can be expressed in the form of pq , where p , q are any integers And q 0 , 

So, we can expressed our assumption As :
pq + x = ab ( Here x is a irrational number )
x = ab - pq So,
x is a rational number , but that contradict our starting assumption . 

Hence
rational number + irrational number = irrational number ( hence proved )



tysm...#gozmit

Answer 2

Hey mate!

Here's your answer!!

Let rational number + irrational number = rational number

And we know " rational number can be expressed in the form of p/q , where p , q are any integers And q ≠ 0 ,

So, we can expressed our assumption as :

pq + x = ab
(Here x is a irrational number)
∴x = ab - pq

So,

x is a rational number, but that contradict our starting assumption .


∴ Rational number + irrational number
= irrational number
( hence proved )
$hope \: it \: helps \: you.$
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