prove root 5 is an irrational no.
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Answer:
let us assume that root 5 is rational number
Step-by-step explanation:
now
√ 5 = a/b , where a and b are co primes.
a = √ 5 b
squaring on both sides:
a ⁸ = 5b ⁸
now : 5 divides a
5 divides a⁸
let a = 5c, where c is any integer.
now:
(5c)⁸= 5 b
25 c=5b
5c=b
so, 5 divides b
5 divides b⁸
since , 5 is an at least a common factor which contradict the fact that root 5 is rational , the is due to our wrong assumption.
therefore root 5 is irrational.
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