Question

Show that 5-root3is an irrational​

Answer 1

Answer:let let 5√3 be rational

Therefore,5√3=a/b(where a and b are co prime)

(5√3)²=(a/b)²

75=a²/b²

75b²=a²

a²is divisible by 75

Therefore, a is division by 75

Therefore,75c= a

Therefore,75b²=(75c)²

75b²=75×75×c²

b²=75c²

Therefore b²is divisible by c²

Therefore b is divisible by c

Therefore both b and a are divisible by c

But a and b are co prime

Therefore our assumption that 5√3is rational was wrong

Therefore 5√3is irrational

Step-by-step explanation: