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A detailed tutorial on how to pick variables. Step by step tutorial including several examples of how to pick variables for reference.

Variables are letters picked to represent unknown values in expressions and equations. Usually they are lowercase, but they can be made uppercase. When trying to pick a variable, you must choose wisely. x is the most common variable, followed by n. x is picked because people associate it with the unknown, and n is picked because it stands for “number.” The variable should be easily recognizable – you should not use a variable that looks like another number or some symbol of a mathematical operation. You should check to see what is included in your equation – for instance, m stands for slope, so if you are doing an equation with slope you need to pick a different variable to avoid confusion. And you should always pick a variable that makes sense – the first letter of your subject matter usually works quite well.

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A detailed tutorial on negative square roots. Step by step tutorial including several examples of negative square roots for reference.

Negative square roots are just like negative numbers. Just like positive and negative numbers have the same true value, only on opposite sides of the number line, negative square roots and positive square roots also have that same property. However, they should not be confused with the square root of a negative number. The square root of a negative number is known as an imaginary number, and is not used in basic algebra. The negative square root is expressed by the square root of a number, with a negative sign in front of the square root symbol, and the square root of a negative number is expressed as a negative number with a square root symbol placed over it.

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A detailed tutorial on the definition of a lemniscate. Step by step tutorial including a visual example of a lemniscate for reference.

A lemniscate is any figure 8 type shape that shows up in mathematics. These figure 8 type shapes are sideways, instead of the normal vertical format of a figure 8. One of the best known lemniscates is the infinity symbol, which resembles a figure 8 tipped on its side.

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A detailed tutorial on the definition of the index of a radical expression. Step by step tutorial including several examples of the index of a radical expression for reference.

A radical expression is what most people know as a square root. The number, variable, or expression inside the square root symbol is referred to as the radicand. What some of you may not realize is that not only are there square roots, there are cube roots, and several other types of roots. These are the exact opposite functions of the exponents. A square root should technically have a little number two on the outside left of the square root symbol. A cube root would have a three there – any number can go there. That is the index.

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A detailed tutorial on identifying the radicand. Step by step tutorial including several examples of how to identify the radicand for reference.

The radicand is associated with what we know as a square root. However, there is a common misconception that a radicand and a square root are the same thing, and they are not. A square root is the entire number – the square root symbol, the number inside, and whatever number it equals. A radicand is simply the number that is inside the square root symbol. For example, take the expression . In this expression, the radicand is ab + 2, because that is what we are taking the square root of.