3 cubed square root of negative 432
What gets cubed? The 3 or "the square root of negative 432" ?
If you mean 3^3 * sqrt (-432), the answer is 561.18 i, where i = sqrt (-1).
To solve the expression "3 cubed square root of negative 432," we need to clarify whether it means "3 raised to the power of 3" or "the cube root of the square root of negative 432."
If the expression is interpreted as "3 cubed times the square root of negative 432" (3^3 * sqrt(-432)), we can evaluate it as follows:
First, find the square root of -432. Since the square root of a negative number is not defined in the real number system, we enter the realm of complex numbers. The square root of -432 can be written as sqrt(432) * i, where i stands for the imaginary unit, sqrt(-1).
Now, we have 3^3 * sqrt(432) * i. Taking the cube of 3, we get 27. Multiplying it by sqrt(432) gives 27 * sqrt(432) * i.
Next, simplify the square root of 432. The square root of 432 can be written as sqrt(16 * 27), which is equal to 4 * sqrt(27). Since there is an i term involved, we have 4 * sqrt(27) * i.
Finally, we multiply 27 and 4, which gives us 108. Thus, the answer to the expression 3 cubed square root of negative 432 (3^3 * sqrt(-432)) is 108i or 561.18i in decimal form.