Show that 5-root3is an irrational
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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:
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