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- Mar 5, 2012

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Hint: we can write $2+8{\sqrt{-5}}=2(1+4\sqrt{-5})$.prove that $2+8{\sqrt{-5}}$ is unit and irreducible or not in $\mathbb Z+\mathbb Z{\sqrt{-5}}$.

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please explain in detail if possibleHint: we can write $2+8{\sqrt{-5}}=2(1+4\sqrt{-5})$.

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What is the definition of a unit?please explain in detail if possible

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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

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

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Not quite.an element alpha belong to k ia called a unit if alpha divisible by 1.

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

$$uv = vu = 1_R,$$

where $1_R$ is the multiplicative identity

Sorry, we are a math help site.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

We do not usually give complete solutions.

Instead we give hints or similar to help people to learn math.

If you're up to it...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.

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?