Question

prove that 5-√3 is irrational​

Answer 1

Answer:

Answer

Let us assume to the contrary 5-root 3 is a rational.

we can find 2 co prime integer a, b (b is not equal to 0 ) such that -

5-root 3= a/b

root 3 = a / b - 5

Note - a and b are integers so, a/b-5 is a rational number and therefore root 3 is also a rational number. but this contradict the fact that root 3 is a irrational number.

so our assumptions is wrong

hence 5-root 3 is a irrational number.