Question

SHOW THAT 5 - ROOT 3 IS IRRATIONAL​

Answer 1

It is just like this question

Answer 2

Answer:

Let us assume that 5√3

Is rational

Therefore it can be expressed in the form a/b (where a and b are co primes)

Therefore 5√3=a/b

5√3b=a. equation 1

Squaring both sides

75b²=a²

b²=a²/75

by fundamental theorem of arithmetic if 75 divides a² then it divides a as well therefore 75 is the factor of a

now let c be any constant

therefore a=75c

from equation 1

5√3b=75c

squaring both sides

75b²=5625c²

c²=75b²/5625

c²=b²/75

so by fundamental theorem of arithmetic 75 is a factor of b as well

Therefore a and b are not co primes as they have common factor as 75 which contradicts the fact that 5√3 is rational.

hence proved it is irrational.