Prove that is irrational.

Question

Prove that is irrational.
The mathematical expression 2 divided by the square root of 7.

Philoid · Accepted Answer

Now, let us assume that 2√7 / 7 is a rational number

⇒ 2√7/7 = p/q (where, p & q are integers, q not equal to 0)

⇒ 2√7 = 7p/q

⇒ √7 = 7p/2q

Here, LHS is an irrational number whereas RHS is a rational number.

So by contradiction 2√7 / 7 is an irrational number