Question

show that 5-root 3 is irrational

Answer 1

If possible let 5-√3 be a rational number equal to a

So, 5-√3=a
(5-√3)^2=a^2 (squaring both the side)
25-10√3+3=a^2
28-10√3=a^2
a^2-28=-10√3
(a^2-28)/-10 =√3

Here a is a rational number so a^2 is a rational number
So a^2-28 is a rational number
So (a^2-28)/-10 is a rational number
So √3 is a rational number because √3=(a^2-28)/-10

But it contradicts the fact that √3 is an irrational number

So our assumption is wrong that 5-√3 is a rational number

So 5-√3 is an irrational number.
Hence proved....

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