Roots

Square Roots

has two equal factors

Square Root Examples

Cube Roots

have three equal factors

Cube Roots

​Reminder about equations...

​Example:

​Our goal is always to UNDO the operations around the variable that we are solving for...

​3x + 4 = 16

​

​ -4

​ -4

​3x = 12

x = 4

​ /3

​ /3

What about square roots?

<-- Opposites -->

The opposite of taking a square root is... squaring!

​Example:

What about CUBE roots?

<-- Opposites -->

The opposite of taking a cube root is... you guessed it: cubing!

​Example:

U2.Classify Real Numbers

by AshleyA 1234567

​Classifying Real Numbers

​Rational Numbers

Can be written as a fraction

​

• Natural Numbers (Counting Numbers)

• Whole Numbers

• Integers

​

​What does this mean: Positive whole numbers, Zero, Negative whole numbers, fractions, mixed numbers, perfect square roots, repeating decimals and terminating decimals are all Rational Numbers.

​Irrational Numbers

​Cannot be written as a fraction

​

Decimals that does not terminate or repeat.

• ​Non-terminating decimals

• ​Non-repeating decimals

​

Hint:​

• Imperfect Squares

• Anything with

​

​Examples:

• ​9.7658128....., -7.109823...., , , , ,

Facts about Rational Numbers

• can be a whole number

• can be a fraction

• can be an integer

• can be a ratio

• can be a repeating decimal

• can be a terminating decimal

• can be a perfect square

Facts about Irrational Numbers

• cannot be written as a fraction or ratio

• non terminating decimal

• non repeating decimal

• non perfect squares

Estimating Irrational Numbers (Non Perfect Squares)

• Step 1: Find the two perfect squares that the irrational number fall between

• Step 2: Find the value of the square root of the perfect squares

Compare and Order Real Numbers

by Robin Parker

​

​How to approximate non-perfect squares using perfect squares:

Compare & Order Real Numbers

• You can compare and order real numbers by writing them in the same notation.

• Write the numbers in decimal notation before comparing and ordering them.