It means that the answer to your square root is negative.
e.g.
√25 = 5
but
-√25 = -5
not to be confused with √-25 which is not a real number.
e.g.
√25 = 5
but
-√25 = -5
not to be confused with √-25 which is not a real number.
To understand this concept, it is important to know that the square root of a negative number is not a real number. In the real number system, the square root of any negative number is undefined. However, mathematicians introduced the concept of imaginary numbers to solve equations where the square root of a negative number appears.
To simplify an expression with a negative sign outside of a square root, you can follow these steps:
1. Identify the number or expression within the square root.
2. Evaluate the square root of that number or expression, treating it as positive.
3. Multiply the result by -1 to account for the negative sign outside the square root.
For example, if you encounter an expression like √(-9), you would follow these steps:
1. Identify that the number within the square root is -9.
2. Evaluate the square root of 9, which is 3.
3. Multiply the result by -1, so the final answer would be -3.
By understanding the concept of imaginary numbers and following these steps, you can handle expressions with negative signs outside the square root.