Square Root of -95

The square root is the inverse of squaring a number. Since -95 is negative, its square root involves imaginary numbers. The square root of -95 can be expressed in terms of the imaginary unit 'i', where i is the square root of -1. Therefore, the square root of -95 is expressed as √-95 = √95 * i, which simplifies to approximately 9.74679i.

Finding the square root of a negative number involves using the imaginary unit 'i'. For non-negative numbers, methods like prime factorization, long division, and approximation can be used. Here we focus on understanding the concept of imaginary numbers for negative square roots.

- Imaginary numbers

- Concept of 'i'

- Simplification

Imaginary numbers are used to represent the square roots of negative numbers. The imaginary unit 'i' is defined such that i² = -1. For any negative number, its square root can be written using 'i'. The square root of -95 is written as √-95 = √95 * i, where √95 is the square root of 95.

To simplify the square root of -95, we separate the negative sign and use the imaginary unit 'i'. Calculate the square root of the positive part (95) and multiply by 'i'.

Step 1: Identify the positive part of the number, which is 95.

Step 2: Calculate the square root of 95, which is approximately 9.74679.

Step 3: Multiply by 'i' to express the result in terms of imaginary numbers: 9.74679i.

Imaginary numbers are used in various fields such as engineering, physics, and complex number theory. They help solve equations that do not have real solutions and are essential in the study of electrical engineering and signal processing.

• Imaginary Number: A number that can be written as a real number multiplied by the imaginary unit 'i', where i² = -1.
   
• Imaginary Unit: The symbol 'i', used to represent the square root of -1, essential in expressing square roots of negative numbers.
   
• Complex Number: A number consisting of a real and an imaginary part, often written in the form a + bi.
   
• Square Root: The value that, when multiplied by itself, gives the original number. For negative numbers, it involves the imaginary unit.
   
• Simplification: The process of expressing a complex mathematical expression in its simplest form, often involving combining like terms and reducing expressions.