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Saturday 15th of June
Calculations with Negative Numbers
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Roots - Radicals 1
Graph of a Line
Sum of the Roots of a Quadratic
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Factoring Trinomials with Leading Coefficient 1
Writing Linear Equations Using Slope and Point
Simplifying Expressions with Negative Exponents
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Solving Quadratic Equations
Parent and Family Graphs
Collecting Like Terms
nth Roots
Power of a Quotient Property of Exponents
Adding and Subtracting Fractions
Solving Linear Systems of Equations by Elimination
The Quadratic Formula
Fractions and Mixed Numbers
Solving Rational Equations
Multiplying Special Binomials
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Polar Form of a Complex Number
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Higher Degrees and Variable Exponents
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Writing a Rational Expression in Lowest Terms
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The Square of a Binomial
Properties of Negative Exponents
Inverse Functions
Rotating an Ellipse
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Linear Equations
Solving Equations with One Log Term
Combining Operations
The Ellipse
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Graphing Inequalities in Two Variables
Solving Trigonometric Equations
Adding and Subtracting Fractions
Simple Trinomials as Products of Binomials
Ratios and Proportions
Solving Equations
Multiplying and Dividing Fractions 2
Rational Numbers
Difference of Two Squares
Factoring Polynomials by Grouping
Solving Equations That Contain Rational Expressions
Solving Quadratic Equations
Dividing and Subtracting Rational Expressions
Square Roots and Real Numbers
Order of Operations
Solving Nonlinear Equations by Substitution
The Distance and Midpoint Formulas
Linear Equations
Graphing Using x- and y- Intercepts
Properties of Exponents
Solving Quadratic Equations
Solving One-Step Equations Using Algebra
Relatively Prime Numbers
Solving a Quadratic Inequality with Two Solutions
Operations on Radicals
Factoring a Difference of Two Squares
Straight Lines
Solving Quadratic Equations by Factoring
Graphing Logarithmic Functions
Simplifying Expressions Involving Variables
Adding Integers
Factoring Completely General Quadratic Trinomials
Using Patterns to Multiply Two Binomials
Adding and Subtracting Rational Expressions With Unlike Denominators
Rational Exponents
Horizontal and Vertical Lines
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nth Roots

Now we will study higher order roots, such as cube roots. Like square roots, these roots can be written using a radical symbol. To indicate the specific root, a number called the index is written just above the on the radical symbol.

For example, the cube root of 8 is written like this: The index, 3, indicates the radical is a cube root.

The cube root of 8 is 2 because 23 = 8. We write:


The square root of a number is also called the 2nd root of the number. The index of a square root is 2, but we rarely write it. Thus,

The cube root of a number is also called the 3rd root of the number.

In a similar way, we define 4th roots, 5th roots, 6th roots, and so on. For example,

• The 4th root of 81 is written like this: . The index is 4. = 3 because 34 = 81.

• The 10th root of 1 is written like this: . The index is 10. = 1 because 110 = 1.

To indicate an nth root, we use the letter n for the index.

• If n is odd, then is always a real number.

For example, and are both real numbers:

• If n is even, then is a real number only when a 0.

For example, , but is not a real number because 5 · 5 -25 and (-5) · (-5) -25.

In fact, no real number multiplied by itself will equal -25.

n nth root symbol
2 square root
3 cube root
4 fourth root
5 fifth root


a. Find      b. Find the 5th root of 243.


a. Find the prime factorization of 625: 625 = 5 · 5 · 5 · 5 = 54 . Since 54 = 625, and 5 is positive, = 5.

b. The 5th root of 243 may be written .  Find the prime factorization of 243: 243 = 3 · 3 · 3 · 3 · 3 = 35. Since 35 = 243, = 3.

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