Question

Prove under root 5 - under root 3 is not a rational no.

Answer 1

Answer:

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$\sqrt{5} - \sqrt{3}$

Let us assume that it is a rational number .

therefore root 5 - roote = p/ q where p and q are integers and q is not equal to 0

now,

root 5 - root 3 = a / b where a and b are co -prime .

root 5 = a / b + root 3

as root 5 is a irrational number. this contracdicts the fact that root 5 is rational .

this is because of our wrong assumption that root 5 - root3 is rational .