Square Root of -87

The square root is the inverse of the square of a number. Since -87 is a negative number, its square root is not a real number. Instead, it is expressed in terms of an imaginary number. The square root of -87 is expressed as √-87 or as an imaginary number, i√87, where i is the imaginary unit. Thus, the square root of -87 is an imaginary number because it involves the square root of a negative number.

The square root of a negative number cannot be found using traditional methods for finding square roots of positive numbers, such as the prime factorization or long division methods. Instead, it is expressed using the imaginary unit 'i'. Here are the steps to express it:

1. Identify the negative number under the square root, which is -87.

2. Express it as a product of -1 and 87: √-87 = √(-1 × 87).

3. Use the property of square roots: √(-1 × 87) = √-1 × √87 = i√87.

Imaginary numbers arise when we take the square root of a negative number. The imaginary unit 'i' is defined such that i² = -1. Therefore, √-87 can be expressed using 'i':

Step 1: Express -87 as a product of -1 and 87.

Step 2: Use the property of square roots: √-87 = √(-1 × 87) = √-1 × √87 = i√87.

The imaginary unit 'i' is used to represent the square root of -1. It allows us to work with square roots of negative numbers in complex number theory. The key property of 'i' is: i² = -1 Using this property, any square root of a negative number can be expressed as a product of 'i' and the square root of the corresponding positive number. For -87, this is i√87.

In the context of complex numbers, a number like √-87 is purely imaginary since it does not have a real part. A complex number is generally expressed in the form a + bi, where 'a' is the real part and 'bi' is the imaginary part. For √-87, it can be expressed as 0 + i√87, where the real part 'a' is 0.

• Square root: The square root of a number 'x' is a value that, when multiplied by itself, gives 'x'. For negative numbers, it involves imaginary numbers.
   
• Imaginary number: A number that can be written as a real number multiplied by the imaginary unit i, where i² = -1.
   
• Complex number: A number in the form a + bi, where 'a' is the real part and 'bi' is the imaginary part.
   
• Imaginary unit (i): A mathematical concept used to denote √-1, allowing the square roots of negative numbers to be expressed.
   
• Real number: Any number that can be found on the number line, including both positive and negative numbers, but not imaginary numbers.