Radical expressions that are identical except for the plus/minus sign in the middle. Expressions like (a
) and (a
) are conjugates. They're sort of the evil twins of the math world.
Multiplication of numbers that distributes over addition and subtraction: a
) = ab
An expression that states the equivalence of two algebraic expressions.
Different equations that have the same solution(s).
A solution to an equation that's formed in the process of simplifying the original equation (for example, taking the square of a radical equation), but is not a valid solution of the original equation. These guys are the worst: they seem like legit solutions when we solve for our variable, but then they run away and scream, "Not!" when we try to plug them back into the equation.
Breaking up an algebraic expression into two or more expressions that can be multiplied together to get the original expression.
Two terms with the exact same radical. If the stuff inside the radical (the radicand) matches, we can combine those terms just like we do with like variables.
Principal Square Root
The positive square root of a number. Way more useful in real-life situations than their negative brethren.
The fact that the sum of the squares of a right triangle's legs is equal to the square of its hypotenuse. Or as most people would prefer to remember it, a2
An equation obtained by setting a quadratic polynomial equal to zero. We can solve these beasts by factoring, completing the square, or busting out the quadratic formula.
A formula for finding the roots of a quadratic equation:
A polynomial of degree two.
An equation with a variable that's contained inside a radical symbol. Usually seen toting around a skateboard and wearing a backwards ball cap.
The symbol of a square root. It sort of looks like a really elaborate check mark: √.
The value inside the radical symbol. For example, 5 is the radicand of
Rationalizing The Denominator
Rewriting the fraction to get rid of the radical in the denominator.
A number raised to the power of two.
The inverse operation of squaring a number.
Values that we can plug into a variable in an equation that make the equation true. Got a problem? Find the solution.
A value that changes. Variables are commonly represented by the letters x
, or z