Question

prove that √7 is an irrational number​

Answer 1

Answer:

let us assume that √7 be rational. thus q and p have a common factor 7. as our assumsion p & q are co prime but it has a common factor. So that √7 is an irrational.

Answer 2

Answer:

√7 is an irrational number

Explanation:

Let us assume that √7 is a rational number

Then, √7=p/q where p and q are integers ans co primes and q not equal to zero

Squaring Both sides

3=p²/q²

p²=3q²

This means that 3 is a factor of p-------(1)

Let p=3a where a is some integer

Squaring both sides

p²=9a²----------(2)

From (1) and (2), 9a²=3q²

q²=3a²

This means that a is factor of q----------(3)

From (1) and (3), a is a factor of both p and q

But we know that p and q are co primes, that is, they do not have any common factor

Therefore, our assumptiom was wrong

Therefore, √7 is irrational