Question

PROVE THAT ROOT4 + ROOT 5 IS AN IRRATIONAL

Answer 1

Let √4+√5 be a rational no. say r
Then √4+√5= r(note that r not equal to 0)
=>√5=r-√4=>(√5)^2=(r-√4)^2
=>5=r^2+4-2√4r=>2√4r=r^2-2
=>√4=(r^2-2)/2r.
As r is rational and r not equal 0, so (r^2-2)/2r is irrational
=>√4 is rational
But this contradicts that √4 is irrational.
Hense, our supposition is wrong.
Therefore, √4+√5 is an irrational number