Question

prove that 5- root 2 is rational
please answer no spamming it's urgent.

Answer 1

Answer:

Let us assume 5-√2 is a rational no.

So , according to the definition of rational no.

5-√2 = a/b where a and b are co-prime and b is not equal to zero.

Now shifting 5 to other side we get

-√2=a/b -5

√2= - a/b+5

√2=(-a+5b)/b

Since a , b and 5 are rational so their addition as well as division would be rational ..

But √2 is irrational and √2 cannot be equal to a rational no.

This contradicts the fact that √ 2 is irrational

This contradiction arises when we 5-√2 as rational

So, 5-√2 is irrational