Question

prove root 5 is an irrational no.​

Answer 1

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$\sqrt{5} is \: a \: irrational \: number$

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Answer 2

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.