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Exponential Decay
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Multiplying and Dividing Fractions 4
Evaluating Expressions Involving Fractions
The Cartesian Coordinate System
Adding and Subtracting Fractions with Like Denominators
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FOIL Method
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Addition Property of Equality
Square Roots
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The Distance Formula
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Fractions
Dividing Mixed Numbers
Evaluating Polynomials
Power of a Product Property of Exponents
Terminology of Algebraic Expressions
Adding and Subtracting Rational Expressions with Identical Denominators
Solving Exponential Equations
Factoring The Difference of 2 Squares
Changing Fractions to Decimals
Solving Linear Equations
Using Patterns to Multiply Two Binomials
Completing the Square
Roots of Complex Numbers
Methods for Solving Quadratic Equations
Conics in Standard Form
Solving Quadratic Equations by Using the Quadratic Formula
Simplifying Fractions 2
Exponential Notation
Exponential Growth
The Cartesian Plane
Graphing Linear Functions
The Slope of a Line
Finding Cube Roots of Large Numbers
Rotating Axes
Common Mistakes With Percents
Solving an Equation That Contains a Square Root
Rational Equations
Properties of Common Logs
Composition of Functions
Using Percent Equations
Solving Inequalities
Properties of Exponents
Graphing Quadratic Functions
Factoring a Polynomial by Finding the GCF
The Rectangular Coordinate System
Adding and Subtracting Fractions
Multiplying and Dividing Rational Expressions
Improper Fractions and Mixed Numbers
Properties of Exponents
Complex Solutions of Quadratic Equations
Solving Nonlinear Equations by Factoring
Solving Quadratic Equations by Factoring
Least Common Multiples
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Solving Exponential Equations
Solving Linear Equations
Multiplication Property of Equality
Multiplying Mixed Numbers
Multiplying Fractions
Reducing a Rational Expression to Lowest Terms
Literal Numbers
Factoring Trinomials
Logarithmic Functions
Adding Fractions with Unlike Denominators
Simplifying Square Roots
Adding Fractions
Equations Quadratic in Form
Dividing Rational Expressions
Slopes of Parallel Lines
Simplifying Cube Roots That Contain Variables
Functions and Graphs
Complex Numbers
Multiplying and Dividing Fractions 1
Composition of Functions
Intercepts of a Line
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Multiplying Two Numbers with the same Tens Digit and whose Ones Digits add up to 10
Factoring Trinomials
Exponents and Polynomials
Decimals and their Equivalent Fractions
Negative Integer Exponents
Adding and Subtracting Mixed Numbers
Solving Quadratic Equations
Theorem of Pythagoras
Equations 1
Subtracting Fractions
Solving Quadratic Equations by Graphing
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Angles and Degree Measure
   
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Finding Cube Roots of Large Numbers

The first thing you need to notice about cubed numbers is how they are formed. For each digit in the number we are cubing, three digits (at most) are formed for the product. We are going to use this configuration to our advantage.

To find the cube root of a number mentally, use the following steps:

Separate the number between the thousands digit and the hundreds digit. The last digit of the number is an indicator of the last digit of the cube root. The following chart gives the last digit of each cube

Notice that 0, 1, 4, 5, 6, and 9, when cubed has the same last digit. Also notice that 2 switched with 8 and 3 switched with 7.

Using all the digits from the left to the thousands place (the left part of the separation), take the cube root of the largest cube less than this number as the digits on the left of the answer.

 

Example:

Find the cube root of 79507.

First, separate the number into two parts, with the dividing line between the thousands and the hundreds: 79 | 507. The number that was cubed to get the ending 7 must have been 3. Therefore, 3 is the last digit of the cube root.

Next, look at the 79. The largest perfect cube less than 79 is 64. The cube root of 64 is 4. Thus, 4 is the first digit.

The cube root of 79507 is 43.

 

Example:

Find the cube root of 884,736. Separate the number into two parts, 884 | 736. The number that was cubed to get the ending 6 must be 6. That makes the last digit of the cube root a 6.

Now, consider 884. The largest perfect cube less than 884 is 729. The cube root of 729 is 9 and that makes 9 is the first digit of the cube root.

The cube root of 884,736 is 96.

 

Example:

Find the cube root of 1,481,544.

Even though there are seven-digits to this number, we still separate the number between the thousands and the hundreds: 1481 | 544. The number that was cubed to get the end 4 must be 4 and thus 4 is the last digit of the cube root.

The largest perfect cube less than 1481 is 1331 and the cube root of 1331 is 11. Therefore, the first numbers must be 11.

The cube root of 1,481,544 is 114.

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