Question

$Prove that 7 \sqrt{5} is an asymmetric number$
is an asymmetric number
​

Answer 1

Answer:

Let us assume that 7

5

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

Answer 2

Step-by-step explanation:

Let us assume that 7√5 is rational number

Hence, 7√5 can be written in the form of a/b where a, b are co-prime and b not equal to 0.

7√5 = a/b

√5 = a/7b

here √5 is irrational and a/7b is rational number.

Rational number ≠ Irrational number

It is contradiction to our assumption 7√5 is rational number.

Therefore, 7√5 is an irrational number.

Hence, proved.