Can a radical be negative when the index is even?
**radicand
The answer is no, if you are working with real numbers. Think about it. Any number raised to an even power is positive.
So, there is no even root of a negative number.
Yes, a radical can be negative when the index is even. When the index is even (such as a square root, fourth root, sixth root, etc.), the radical can represent both positive and negative values. This is because when you raise a negative number to an even power, the result is always positive.
To determine if a radical can be negative when the index is even, you need to consider the number being radicand. If the radicand (the number inside the radical) is positive, the result of the radical will be both positive and negative. However, if the radicand is negative, the result will be complex (imaginary) and the radical cannot be represented in real numbers.
For example, the square root of 9 can be written as √9. Since 9 is a positive number, the square root of 9 is both +3 and -3. However, the square root of -9 (√-9) is not a real number because the radicand is negative.