Question

prove that 7root5 is an irrational number

Answer 1

Step-by-step explanation:

let 7√5 be a rational number

Then

7√5 = p/q

(CP and q are Co - prime number and q = O )

√S =P/ 7 q

As, we can se that P /7q is a rational so √5

should also be rational . But this contradict the fact that √5 is irrational.

So, by this we can say that 7√ is an irrational number

Thank you

I Hope is helpful for you

Answer 2

Step-by-step explanation:

Let us assume that 7

is rational number

Hence 7 ,5 can be written in the form of

b

a

where a,b(b



=0) are co-prime

⟹7

5

=

b

a

⟹

5

=

7b

a

But here

5

is irrational and

7b

a

is rational

as Rational



=Irrational

This is a contradiction

so 7

5

is a irrational number