find the cube root of negative 8 3 square root of negative 8
The cube root of -8 is -2, since -2 × -2 × -2 = -8.
The square root of -8 is not defined in the real number system because the square root of a negative number is not a real number. In the complex number system, the square root of -8 is written as √(-8) = 2i√2, where i represents the imaginary unit.
To find the cube root of a number, you can follow these steps:
1. Start by recognizing that the cube root of a number x is a value that, when multiplied by itself twice, gives you x. Mathematically, it can be written as ∛x.
2. In the given case, you want to find the cube root of -8. Since -2 x -2 x -2 equals -8, the cube root of -8 is -2.
Now, let's move on to the second part of your question: finding the square root of -8√3.
1. First, simplify the expression within the square root. Inside the square root, √(-8) can be written as √(-1 x 2 x 2 x 2), which simplifies to 2i√2. Here, "i" represents the imaginary unit, which is the square root of -1.
2. Now, combine the simplified expression inside the square root (√2) with the remaining √3 outside the square root, giving you 2i√2√3.
So, the square root of -8√3 is equal to 2i√6.