Is the square root of 8 irrational

The square root of 8 is an irrational number

Answer and Explanation:

The square root of 8, or √ (8), is 2√ (2).

The square root of a number a is a number that when multiplied by itself gives a. In other words, √ (a) = b if b * b = a.

If we plug √ (8) into our calculator, we will get a very long decimal that is rounded to a specific decimal place, so it is not an exact answer.

√ (8) ≈ 2.8284271247 ...

This is because √ (8) is an irrational number. When this is the case, we can find an exact answer of √ (a), where a is not a perfect square, by simplifying the square root. To do this, we use the following steps and rules:

If possible, rewrite a as a product of a perfect square and another number. If this is not possible, then the square root is as simplified as possible.

Break the square root up using the rule that √ (a * b) = √ (a) * √ (b).

Evaluate the square root that is a perfect square.

Repeat the entire process for the square root that is not a perfect square until it cannot be simplified any further.

Therefore, to simplify √ (8), we first rewrite 8 as a product of a perfect square and another number. The number 4 is a perfect square and a factor of 8, so we can rewrite 8 as 4 * 2:

√ (8) = √ (4 * 2)

We now use our rule to break up the square root:

√ (4 * 2) = √ (4) * √ (2)

Now we evaluate √ (4) as 2 (because 2 * 2 = 4):

√ (4) * √ (2) = 2 * √ (2) = 2√ (2)

Because 2 doesn't have any perfect square factors, √ (2) is as simplified as possible. Therefore, √ (8) is equal to 2√ (2).