Final answer:
When simplifying any expression involving square roots, it is important to look for perfect square factors. In this case, 8 can be rewritten as 4*2, and j⁸ can be rewritten as (j⁴)². Therefore, the square root of 8j⁸ can be rewritten as the square root of 4 times the square root of 2 times j⁴ times j⁴. The square root of 4 is 2, and the square root of j⁴ is simply j². This leaves us with the final answer of 2j⁴.
Explanation:
When simplifying any expression involving square roots, it is important to look for perfect square factors. In this case, 8 can be rewritten as 4*2, and j⁸ can be rewritten as (j⁴)². Therefore, the square root of 8j⁸ can be rewritten as the square root of 4 times the square root of 2 times j⁴ times j⁴. The square root of 4 is 2, and the square root of j⁴ is simply j². This leaves us with the final answer of 2j⁴.
To further explain this, we can break down the calculation step by step. Firstly, we can rewrite 8j⁸ as (4*2)j⁸. Using the property of square roots, we can split the square root of 8j⁸ into the square root of 4 times the square root of 2 times the square root of j⁸. The square root of 4 is 2, and the square root of j⁸ can be rewritten as (j⁴)², which is equal to j⁸. This leaves us with 2 times the square root of 2 times j⁸. Since j is greater than or equal to zero, we can rewrite j⁸ as (j⁴)². The square root of (j⁴)² is simply j⁴. Therefore, our final answer is 2j⁴.
In summary, when simplifying expressions involving square roots, it is important to look for perfect square factors. In this case, we were able to simplify the square root of 8j⁸ to 2j⁴ by rewriting 8 as 4*2 and j⁸ as (j⁴)². This allowed us to reduce the expression to 2 times the square root of 2 times j⁸, which can be further simplified to 2j⁴. It is important to follow the proper order of operations and apply the properties of square roots to accurately simplify expressions.