Is $2 + 8\sqrt{-5}$ a Unit or Irreducible in $\mathbb{Z} + \mathbb{Z}\sqrt{-5}$?

[abs1]

prove that $2+8{\sqrt{-5}}$ is unit and irreducible or not in $\mathbb Z+\mathbb Z{\sqrt{-5}}$.

 

[I like Serena]

prove that $2+8{\sqrt{-5}}$ is unit and irreducible or not in $\mathbb Z+\mathbb Z{\sqrt{-5}}$.

Hint: we can write $2+8{\sqrt{-5}}=2(1+4\sqrt{-5})$.

 

[abs1]

Hint: we can write $2+8{\sqrt{-5}}=2(1+4\sqrt{-5})$.

please explain in detail if possible

 

[I like Serena]

please explain in detail if possible

What is the definition of a unit?

 

[abs1]

an element alpha belong to k ia called a unit if alpha divisible by 1.
dear it is my question if u not solved it then no problem its ok .if u solved it then give me complete explanation thank u so much
irreducible element:a non zero non unit element alpha belong to k is said to be irreducible if aplha=ab.
either a is unit or b is unit.
i give u both def. of unit and irreducible thank u so much

 

[I like Serena]

an element alpha belong to k ia called a unit if alpha divisible by 1.

Not quite.
From wiki:

a unit in a ring with identity $R$ is any element $u$ that has an inverse element in the multiplicative monoid of $R$, i.e. an element $v$ such that
$$uv = vu = 1_R,$$
where $1_R$ is the multiplicative identity​

dear it is my question if u not solved it then no problem its ok .if u solved it then give me complete explanation thank u so much

Sorry, we are a math help site.
We do not usually give complete solutions.
Instead we give hints or similar to help people to learn math.

irreducible element:a non zero non unit element alpha belong to k is said to be irreducible if aplha=ab.
either a is unit or b is unit.

If you're up to it...

The hint I gave showed that we can split the expression in two factors that we might call $a$ and $b$.
Let's start with $2$.
Is it a unit? That is, does it have a multiplicative inverse in the given ring?