Square Root of -112

The square root is the inverse of the square of the number. Since -112 is a negative number, its square root is not a real number. In the context of complex numbers, the square root of -112 is expressed in terms of an imaginary unit 'i'. The square root of -112 can be written as √(-112) = √112 * i. In its simplified form, this is approximately 10.583 * i, which is an imaginary number because it involves i, representing √(-1).

For real numbers, negative numbers do not have real square roots. Instead, we use complex numbers to express the square root of a negative number. The process involves finding the square root of the positive counterpart and then multiplying by 'i'. The methods such as prime factorization, long division, or approximation are not directly applicable to negative numbers in real terms but can be used to find the square root of the positive part.

To find the square root of a negative number like -112, we first find the square root of the positive part, 112, and then attach the imaginary unit 'i'.

Step 1: Find the square root of 112. The approximate square root is 10.583.

Step 2: Multiply by 'i' to convert it to the imaginary form. So, √(-112) = 10.583 * i.

Since -112 does not have a real square root, we focus on the positive counterpart 112 for approximation.

Step 1: The square root of 112 is approximately 10.583.

Step 2: Multiply this result by 'i' to get the square root of -112, which is 10.583 * i.

The imaginary unit 'i' is defined as the square root of -1. In complex numbers, 'i' is used to express the square roots of negative numbers.

For example, the square root of -112 is expressed as 10.583 * i.

• Square root: The square root is a value that, when multiplied by itself, gives the original number. For negative numbers, it involves 'i'. Example: √(-16) = 4 * i.
   
• Imaginary number: An imaginary number is a number that can be expressed as a real number multiplied by the imaginary unit 'i'. Example: 3 * i.
   
• Complex number: A complex number consists of a real part and an imaginary part. Example: 4 + 5 * i.
   
• Perfect square: A perfect square is an integer that is the square of an integer. Example: 16 is a perfect square because it is 4 squared.
   
• Integers: Whole numbers and their negatives. Examples include -3, 0, 7.