Question

show that root 7 is irrational

Answer 1

i gave for 5 but 7 also same method

Answer 2

we will prove it by using contradiction method

let √7 be rational say p/q ( where p and q are co prime)

√7=p/q

on squaring

7 = p^2 /q^2

7 q sq = p sq

as 7 is divisible by 7 q sq

it is divisible by p sq

p is prime

7 is divisible by p

now

let p be 7 k ( where k is real no)

putting value in 7q sq = p sq

7 q ^ 2 = ( 7 k)^2

7 q^2 = 49 k ^2

q^ 2= 7 k^2

as 7 is divisible 7 k^2

7 is divisible by q^2

q is prime

7 is divisible by q

Both p and q have common factor

so there is contradiction

our assumption is wrong

√ 7 is irrational

Hope this helps