Question

prove that √5 is an irrational number​

Answer 1

Step-by-step explanation:

Let root 5 be a rational n

So, √5=a/b. B not equal to 0

A and b have common factor than 1

By squaring, 5^2b=a^2

So, 5 divides a^2. Then 5 also divide a. By(theorem 1.3)

Let. A=5c. By squaring ==a^2=25c^2

By putting the value of a

=25c^2=5b

5^2c=b^2

Sane, 5divide b^2.also 5 divide b

So, this contradict that a and b have 5 as comment factor

But this contradict that a and b have 1 as comn factor

This contradiction arisen of our incorrect assumption that √5 is rational

So, √5 is irrational

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Answer 2

Answer:

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