# Rules for Radicals — the Algebraic Kind

### Part of the Algebra II For Dummies Cheat Sheet

Working with radicals can be troublesome, but these equivalences keep algebraic radicals from running amok. Finding the root of product or quotient or a fractional exponent is simple with these formulas; just be sure that the numbers replacing the factors *a* and *b* are positive.

An operation that tells you how far a number is from zero.

The number with the same numerical part but the opposite sign (plus or minus) of a given number. If zero is the sum of two numbers, then these two numbers are additive inverses of one another.

A characteristic of addition and multiplication that allows the grouping of terms to change without affecting the result.

A value multiplied repeatedly in an exponential expression.

A process requiring two values to produce a third value.

Two terms separated by addition or subtraction.

A grouping symbol that looks like this: { }.

A grouping symbol that looks like this: [ ].

A number multiplied by a variable. The coefficient precedes the variable.

A method of counting that tells how many ways a designated number of objects can be selected from a given set.

The same value on the bottom of more than one fraction.

A characteristic of addition and multiplication that allows the order of the values in an operation to be changed without affecting the result.

A whole number larger than 1 that isn’t prime.

A variable or number that never changes in value in an expression.

The third power of a number; the result of multiplying a number by itself three times.

A number that you can multiply by itself three times to get a given number. For example, the cube root of 8 is 2, because 2 times 2 times 2 equals 8.

An adjective that describes an expression in which the highest power is three.

A fraction with an unwritten denominator of 10 indicated by the decimal point.

The highest power occurring in an expression.

The bottom number in a fraction.

The result of subtraction.

Numerals from zero through nine, so called because they were originally counted on the fingers.

A characteristic of multiplication and addition that allows for the multiplication of each individual term in a grouped series by a term outside of the grouping without changing the value of the expression.

A number to be divided by another number.

A number that can be divided by another number with no remainder.

A solution that appears twice when solving an equation because the related factor appears twice in the factored form. For example, in (*y *– 2)(*y* – 2) = 0, *y* = 2 is a double root or solution. In (*y *– 2)(*y *– 2)(*x* + 3) = 0, *y* = 2 is still a double root or solution.

A mathematical statement with an equal sign showing that two values are equal.

Fractions equal to one another, even though they may have different denominators.

A number that can be divided by 2.

A value in smaller type found above and to the right of the base that indicates the number of times the base is multiplied by itself.

Any combination of values (variables, numbers, and/or constants) and operations that can be used to show how things belong together and compare to one another.

1. (noun) Any of the values involved in a multiplication problem that when multiplied together produces a result. 2. (verb) To rewrite an algebraic expression as a product.

An operation that multiplies a whole number by every counting number smaller than the whole number.

1. An acronym for first, outer, inner, and last — which indicates the order in which two terms (one from each of two binomials) are multiplied together. 2. The process of multiplying two binomials.

A rule or method that is accepted as true and used over and over in common applications.

Any quantity expressed as a numerator (the value above the fraction line) and a denominator (the value below the fraction line).

A line separating the numerator from the denominator in a fraction.

The largest possible value that evenly divides each term of an expression containing two or more terms.

Parentheses, brackets, and braces that can affect the order of operations. Terms and operations within the grouping symbol take precedence.

Terms and operations within grouping symbols.

A fraction whose numerator is larger than the denominator.

A relationship between two unequal values.

Without end; uncountable, as in a repeating decimal.

A positive or negative whole number or zero; numbers starting with zero and going up or down in increments of one.

A number with no fractional equivalent whose decimal never repeats or terminates.

An adjective describing an expression or equation in which the highest power of any variable is one. Constants can be higher powers.

The status of a fraction whose numerator and denominator cannot be divided evenly by the same number.

An improper fraction written as a whole number alongside a fraction.

An expression with only one term.

A number evenly divisible by a specific factor.

A rule stating if the product of two numbers is zero, then one of the numbers must be zero.

Also known as a reciprocal, one of two numbers whose product is one. The reciprocal of a number is that particular number in the denominator of a fraction with a value of one in the numerator.

An integer multiplied with both the numerator and denominator of a fraction.

Values starting with one and increasing by one.

Any quantity that is less than zero; it is usually preceded by a minus sign.

Two numbers, one positive and one negative, whose product is –1.

A condition where two or more grouping symbols are inside one another.

A set of numbers.

The top number in a fraction.

A whole number that is not evenly divided by 2.

A mathematical process, such as addition, subtraction, multiplication, and division, performed on one or more quantities.

Fractions with a denominator of 100. The percentage is the numerator of the fraction, indicating the number of parts out of 100.

A counting method that determines the number of ordered arrangements there are when a certain number of objects are selected from a given set.

An expression with one or more terms.

Any quantity greater than zero.

A value of an exponent indicating the number of times the base is multiplied by itself.

A rule of exponents, where any number raised to the power of zero equals one as long as the base number isn’t zero.

The process of finding the prime numbers that, when multiplied together, produce a given composite number.

A whole number larger than one that can be divided evenly only by itself and one.

A positive number that when multiplied by itself produces a given positive number.

The result of multiplication.

A fraction whose value is less than one; thus, the numerator is always smaller than the denominator.

An equation showing that two ratios are equal to one another.

Also known as *second degree**,* an expression or equation in which the highest power is 2.

The result of division.

The symbol for the operation to find a square root.

Multiplying a base number the number of times indicated by the exponent.

A quantity, positive or negative, that can be written as a fraction; its decimal equivalent terminates or repeats.

Any rational or irrational number.

1. Two numbers whose product is always one. 2. Either one of the two numbers in a reciprocal.

To divide out a common factor of the numerator and denominator of a fraction, leaving an equivalent fraction.

The condition of two numbers that have no factors in common other than the number one.

A value that is left over when one number is divided by another.

A decimal in which, beyond a certain point, a digit or set of digits repeats indefinitely.

A value that, multiplied by itself a number of times, results in the value or number wanted.

Approximating a value to the nearest digit or decimal place.

A standard way of writing very large and very small numbers as the product of two values — a number between 1 and 9 and a power of 10. Scientific notation follows the form *N* × 10*a** *where *N *is a number from 1 up to 10, but not 10 itself, and *a *is an integer (positive or negative number).

A symbol indicating whether a value is positive (+) or negative (−).

A fraction in which both the numerator and the denominator are whole numbers.

To combine all that can be combined in an expression or equation, and put it in its most easily understandable form.

Value(s) of a variable that make an equation a true statement.

Find the answer or the number that a variable stands for.

1. The product of another number times itself. 2. A value with an exponent of 2.

A value resulting when a given value is multiplied by itself.

A method of replacing a value with its equivalent.

The result of addition.

A characteristic of equations that allows for the exchange of the value(s) on one side of the equal sign with the value(s) on the other side (quantities on the right go to the left; quantities on the left go to the right) without changing the truth of the equation: If *x* = *y,* then *y* = *x.*

A short-cut division process in which only the coefficients of the terms in an expression are used. The answer is obtained by multiplying and adding.

A group of number(s) and/or variable(s) connected to one another by multiplication or division and separated from other terms by addition or subtraction.

An expression with three terms. Each term is separated from the others by addition or subtraction.

To factor a trinomial into two binomials.

A numeric equivalent or worth of an expression or variable.

A letter representing an unknown number or what you’re solving for in an algebra problem.

All natural numbers plus zero.