Question

prove that ^5 is an irrational number.
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Answer 1

Answer:

Let us assume, that √5 is rational number.

i.e. √5 = x/y (where, x and y are co-primes)

y√5= x

Squaring both the sides, we get,

(y√5)2 = x2

⇒5y2 = x2……………………………….. (1)

Thus, x2 is divisible by 5, so x is also divisible by 5.

Let us say, x = 5k, for some value of k and substituting the value of x in equation (1), we get,

5y2 = (5k)2

⇒y2 = 5k2

is divisible by 5 it means y is divisible by 5.

Therefore, x and y are co-primes. Since, our assumption about is rational is incorrect.

Hence, √5 is irrational number.

Answer 2

Step-by-step explanation:

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