Question

show that root5 is irrational

Answer 1

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Answer 2

hey mate,

Let of possible we suppose that√5 is a rational number√5=a/b. (where a and b are the co-primes and i.e. b is not equal to 0)

on squaring both sides

(√5)^2 =(a/b)^2

5=a^2/b^2

5b^2=a^2------------(i)

a^2 is divisible by 5

5 is a factor of a

now, a=5c

a^2=(5c)^2=25c^2

put the value of a^2 in eq. (i)

5×b^2=25c^2

b^2=25c^2/5

=5c^2

5 is factor of b^2

5 is factor of b

5 is common factor of a and b

this contradicts the fact that √5 is a rational no. our supposition is wrong.

Thus, √5 is an irrational no.

( a and b have no common factor other then 1).

hope it helps you..

if u satisfy my sol. then mark me as a brainlist.