# Squares and Square Roots

# Squares and Square Roots Examples

#### Squares

Remember roots? Not the tree things that you trip over all the time, the excellent television miniseries, or the Canadian apparel company. Roots are the solutions to polynomials that are set equal...

#### Multiplication

To multiply radicals, we multiply the radicands. Math can be straightforward, too. Who knew?Sample ProblemThis makes sense because a square root of 20 is a number that gives us 20 when multiplied b...

#### Division

These square roots are nice and everything, but it would be nicer if we could turn them into fractions on top of it. It's like we can read your mind, right? Spooky.To divide radicals, we divide the...

#### Addition and Subtraction

To add or subtract radical expressions, simplify each radical term and then combine like terms. A simplified radical term consists of a coefficient and a radical, under which there is a radicand. C...

#### Multiplication

Multiplication of radical expressions is similar to multiplication of polynomials. Remember what a gas that was? Now we can experience that thrill ride all over again, and you don't even need to wa...

#### Division

We already know how to divide one radical term by another, and how to simplify our answer by rationalizing denominators. However, because you looked sleepy the last time we went over it, let's revi...

#### Taking Square Roots

The easiest possible quadratic equation to solve would be something like x2 = 9, so we won't be dealing with anything more complicated than that. Psych! (Sorry.)If the square of x is 9, then x can...

#### Completing the Square

Now we know how to solve a quadratic equation that can be rearranged so we have the square of a degree 1 expression on one side and a number on the other side. We also know how to solve quadratic e...

#### Quadratic Formula

Let's kick things off with a...Sample Problem!What, you were expecting a party?Solve the quadratic equation ax2 + bx + c = 0 by completing the square. Here we know a, b, c are numbers, but we do...

#### Solving Radical Equations

A radical equation is an equation that features a variable contained inside a radicand. At least it won't get wet if it rains.An example of a radical equation is .The equation is not a radical equ...