Final answer:
The real solution of the equation x^5 = -48 is approximately -2.63 when rounded to two decimal places, as it represents the fifth root of -48.
Step-by-step explanation:
To find the real solution(s) of the equation x^5 = -48, you must find the fifth root of -48. Since -48 is a negative number and we're looking for a real solution, it means we're dealing with a single real root (as complex roots come in pairs).
The fifth root of -48 can be found by taking the fifth root of 48 and then applying the negative sign, which is equivalent to -∛48. To express this with a decimal approximation, we would get:
x ≈ -2.626527803. However, when we round that to two decimal places, we have:
x ≈ -2.63
Therefore, the real solution to x^5 = -48 is approximately -2.63.