Question

prove that√5 is irrational​

Answer 1

Answer:

yes it is

Step-by-step explanation:

Answer 2

Answer:

it is an easy proof

To prove√5 is irrational, let us take √5  is rational

if so √5 =a/b  [a and b are coprimes]

       b√5 =a

      $b^25=a^2$     [squaring on both sides]

     this shows $a^2$ is divisible by 5, then a is also divisible by 5..............(1)

then by above statement, a=5c [c is any positive number]

                                     $a^2=(5c)^2$

                                   $b^2$$5=25c^2$

                                    $b^2=5c^2$

 this shows $b^2$ is divisible by 5, then b is also divisible by 5.....................(2)

we said above a and b are coprimes this contradicts with (1) and (2) as a and b have atleast 5 as coomon factor

so our assumption is false so √5  is irrational

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