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Recursos > roots and radicals

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Imaginary Numbers

"An imaginary number bi has two parts: a real number, b, and an imaginary part, i, defined as i^2 = -1. Imaginary numbers are applied to square roots of negative numbers, allowing them to be simplifi ...

How to Multiply Radicals

"To simplify two radicals with different roots, we first rewrite the roots as rational exponents. Before the terms can be multiplied together, we change the exponents so they have a common denominator ...

Solving Radicals

"Solving equations with radicals, no matter what power, involves isolating the radical on one side of the equation and then raising both sides of the equation to the power of the radical. When solvin ...

Evaluating Rational Exponents

"Rational exponents indicate two properties: the numerator is the base's power and the denominator is the power of the root. When evaluating rational exponents it is often helpful to break apart the e ...

Simplifying Radicals

"When simplifying roots that are either greater than four or have a term raised to a large number, we rewrite the problem using rational exponents. Remember that every root can be written as a fractio ...

Dividing Complex Numbers

"Fractions with negative roots in the denominator or with i in the denominator must be rationalized (since i represents a square root). When dividing complex numbers with negative roots, simplify in t ...

Rationalizing a Denominator

"When rationalizing a denominator with two terms, called a binomial, first identify the conjugate of the binomial. The conjugate is the same binomial except the second term has an opposite sign. Nex ...

Rationalize the Denominator

"When a denominator has a higher root, multiplying by the radicand will not remove the root. Instead, to rationalize the denominator we multiply by a number that will yield a new term that can come ou ...

Rational Exponents with Negative Coefficients

"A negative coefficient of a term with a rational exponent can mean that we either (1) apply the rational exponent and then take the opposite of the result, or (2) the rational exponent applies to a n ...

Rational Exponents

"Any radical can also be expressed as a rational exponent. For example, a cube root is equivalent to an exponent of 1/3; a fourth root is an exponent of 1/4. When using this method to simplify roots, ...

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