Simplify: i^25
Sqrt-900
cuberoot-125x^6
i^2=-1
i^3 = -i
i^4 = 1
Do you notice a trend (to get to i^25)?
sqrt -900 = sqrt (-1*900) = 30i
You can check this and your work by going to google and typing in the equation; e.g., i^25 or sqrt -900 and enter.
To simplify these expressions, let's break them down one by one.
1. Simplifying i^25:
Remember that the imaginary unit i is defined as the square root of -1. It follows a pattern where i^1 = i, i^2 = -1, i^3 = -i, and i^4 = 1. After i^4, the pattern repeats every four powers.
In this case, i^25 can be reduced by dividing the exponent by 4, leaving us with a remainder of 1. So, i^25 is equivalent to i^1, which is simply i.
Answer: i^25 = i
2. Simplifying sqrt(-900):
To simplify this expression, let's first find the square root of 900. The square root of 900 is 30, as 30*30 = 900.
However, we have a negative sign in front of the square root, which means we need to consider the imaginary number. Taking the square root of a negative number gives us an imaginary number. In this case, sqrt(-900) = 30i.
Answer: sqrt(-900) = 30i
3. Simplifying cuberoot(-125x^6):
Let's tackle this expression step by step. First, simplify the cuberoot(-125):
Cuberoot(-125) = -5
Next, let's consider the x^6 term. As it is raised to the power of 6, it will remain unchanged:
Cuberoot(-125x^6) = -5x^6
Answer: cuberoot(-125x^6) = -5x^6