# What is the irrational conjugate of 1+sqrt8? complex conjugate of 1 + sqrt(-8)?

Aug 15, 2016

$1 - \sqrt{8} \mathmr{and} 1 - \sqrt{- 8} = 1 - i \sqrt{8}$, where i symbolizes $\sqrt{- 1}$.

#### Explanation:

The conjugate of the irrational number in the form

$a + b \sqrt{c}$,

where c is positive and a, b and c are rational (including computer

string-approximations to irrational and transcendental numbers) is

a-bsqrt c#'

When c is negative, the number is termed complex and the

conjugate is

$a + i b \sqrt{| c |}$, where$i = \sqrt{- 1}$.

$1 - \sqrt{8} \mathmr{and} 1 - \sqrt{- 8} = 1 - i \sqrt{8}$, where i symbolizes $\sqrt{- 1}$