Question

show that (4-✔3）is irrational

Answer 1

Let
$4 - \sqrt{3}$
Be rational than
4-root 3=p/q
Root3=p/4q
Thus root three is irrational and p/4q is rational. So,.
$4 \sqrt{3 \:}$
Is irrational

Answer 2

Consider, 4−√3
Let 4−√3 = (a/b) a rational number
⇒ −√3 = (a/b) − 4
⇒ −√3 = (a − 4b)/b
⇒ √3 = (a − 4b)/(−b)
Since a, b are integers, then (a − 4b)/(−b) represents a rational number.
But this is a contradiction since RHS is a rational number where as LHS (√3) is an irrational number
Hence our assumption that " 4−√3 = (a/b) is a rational number" is incorrect.
Thus 4−√3 is an irrational number .

If you find it useful then mark it as brainliest! ☺️