Is every irrational a surd

sqrt(8) = /(8) = sqrt(2 x 4) =>

sqrt(2 x4) = sqrt(2) X sqrt(4) => sqrt(2) X 2 =>

2*sqrt(2)

'2' is a Prime number.

The 'Square Roots' of prime numbers are IRRATIONAL.

sqrt(2) = 1.414213562.... ( to infinity). This makes it irrational .

Hence

2 * 1.414213562.... = 2.828427125..... (Which is also irrational).

NB A rational number multiplied to an irrational number produces an irrational result,.