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).
