Question

prove that route 7 is an irrational number ?

Answer 1

Answer:

Step-by-step explanation:

Hi

Answer 2

Answer:

Let us assume the contrary that root 7 is rational.

Then,

It would be of the form a÷b

root 7=a÷b (a and b are integers and b is equal to 0).

a and b have common factors other than 1 then divide them by the common factors to make them coprime.

(root7) ^2=(a÷b) ^2 (squaring on both sides)

7=a^2÷b^2

7b^2=a^2

a^2 divides 7b^2

Then a will also divide 7b.

Taking a=7c

root7b=7c

(root7b) ^2=(7c) ^2 (squaring on both sides)

7b^2=49c^2

b^2=7c^2

b^2 divides 7c^2

then b also divides 7c.

Hence a and b must have at least 7 as its factor which contradicts the fact that a and b are coprime.

This contradiction has arisen due to our wrong assumption that root 7 is rational.

Therefore root 7 is rational