Final answer:
The square root of 8 in simplified radical form is 2√2. This is found by factoring 8 into 4 and 2, and recognizing that 4 is a perfect square with a square root of 2.option b is correct answer.
Step-by-step explanation:
The question you've asked concerns finding the square root of 8 in simplified radical form. To simplify √8, we look for perfect square factors. The number 8 can be factored into 4 × 2, where 4 is a perfect square. Taking the square root of both 4 and 2, we get √4 × √2, which simplifies to 2√2 since √4 is equal to 2. Therefore, the simplified radical form of √8 is 2√2.
To better understand this concept, consider an expression with a perfect square. For instance, when we take the square root of x², the result is 'x' because when 'x' is squared (²), it implies that 'x' is multiplied by itself.
Therefore, when we decompose 8 into its factors and look for squares, we isolate 4 because squaring 2 gives us 4. Thus, √8 = √(4×2) = √4√2 = 2√2, which is option (b) in your list of potential answers.