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Simplify
Solution:
Consider the given equation above
This equation is considered a difficult one because the index of a radical is 6. We need to think a number that is raised to the sixth power will give an answer of 576. If 2 raised to the sixth power, the answer is 64. If 3 raised to the sixth power, the answer is 729. We cannot use 3 because 729 is greater than 576.
If we divide 576 by 2, the answer is 288. Again, if we divide 288 by 2, the answer is 144. The factors of 576 are 4 and 144. 4 and 144 are perfect squares. We can rewrite the above equation as follows
As you noticed that the exponent of 2 is a multiple of 6 while the exponent of x is not. We need to factor and rewrite x into a multiple of 6 as follows
Take the sixth root of the terms with exponents that are multiples of 6, we have
The remaining terms inside the radical have even exponents. Since the index of a radical is 6, we need to further simplify the radical as follows
Therefore, the final answer is
