Can you have a negative square root

Ben Johnson mk2 Ben Johnson mk2 1 1 gold badge 2 2 silver badges 6 6 bronze badges. The terms "real" and "imaginary" are historical vestiges from a time when mathematicians were skeptical about the legitimacy and meaning of complex numbers.

Today complex numbers are completely accepted, we have far more general abstract algebraic machinery than them nowadays, and they are applicable to the real world.

Teachers may tacitly understand "numbers" to mean "real numbers" to keep their lessons focused on that level of math for students. This might be a starting point.

A thing is not the same as the algorithm if any used to compute it. Add a comment. Active Oldest Votes. Neal Neal 30k 2 2 gold badges 61 61 silver badges bronze badges. A bit nitpicky but relevant for this topic. So it is very important to specify which set of numbers you are talking about! Henry Swanson Henry Swanson Christian Chapman Christian Chapman 4, 2 2 gold badges 22 22 silver badges 41 41 bronze badges.

By the way, I doubt that anybody wants to define a number as "the" solution and to discover right away that if there are solutions, there are at least two. Keter Keter 1. Are you convinced this short treatment has added something to the Answers previously given?

If so, it would be helpful to Readers to emphasize or highlight exactly what is being introduced for the first time. Full answer with tables and graphs www. Georgi Georgi 1 2 2 bronze badges. Square definition:"In mathematics, a square is the result of multiplying a number by itself. In this case, the sign asks you to find which factor can be multiplied by itself twice to equal the expression inside the radical. The expression inside the radical is also called the radicand.

Anatomy of a Radical Expression. Radical expressions are expressions that include values within a radical sign.

All positive real numbers has two square roots, one positive square root and one negative square root. The positive square root is sometimes referred to as the principal square root. The reason that we have two square roots is exemplified above.

The product of two numbers is positive if both numbers have the same sign as is the case with squares and square roots. If the square root of an integer is another integer then the square is called a perfect square.

For example 25 is a perfect square since. Imaginary Unit Number. When doing arithmetic on i , treat it as you would an " x".

Do NOT confuse "irrational" numbers with "imaginary" numbers. They are NOT the same. A complex number is a real number a , or a pure imaginary number bi, or the sum of both.

NOTE: The re-posting of materials in part or whole from this site to the Internet is copyright violation and is not considered "fair use" for educators.

Please read the " Terms of Use ". The imaginary number " i " is the square root of negative one.