Chapter 7 Real Numbers Test Review

Chapter 7 Real Numbers Test Review

Squares, Cubes, Rational, Irrational

Decimals help us compare numbers

• Decimals that end are also called Terminating Decimals

• Decimals that have a pattern or are in bar notation are also called Repeating Decimals

Multiple Select

Terminating decimals stop or end. Convert all numbers to decimals and

Select all Terminating decimals

• $\frac{1}{5}$

• $.\overline{4}$

• $0.125$

• 0.454...

Multiple Select

Repeating decimals have a pattern or are written in bar notation. Convert all numbers to decimals and

Select all Repeating decimals

• $\frac{1}{6}$

• $0.33$

• $.\overline{2}$

• $\frac{2}{3}$

Rational vs. Irrational

• Rational Numbers - Fractions, Terminating Decimals, Repeating Decimals, Perfect Roots

• Irrational Numbers - Decimals that never end or have no patter (Mumbo Jumbo), Non perfect roots

Multiple Select

Choose the Rational Numbers

• $\frac{4}{5}$

• 0.25

• $\sqrt{16}$

• $0.\overline{8}$

• $\sqrt{30}$

Multiple Select

Choose the Irrational Numbers

• $\frac{3}{11}$

• $2\pi$

• $-\sqrt{100}$

• $0.123456\ldots$

Perfect Squares & Roots

• No index - It is a square root

• Follow the sign in front of the radical sign

Multiple Select

Select the roots that have only a positive value. 

•  $\sqrt{121}$  

•  $-\sqrt{\frac{1}{36}}$  

•  $\pm\sqrt{\frac{289}{49}}$  

•  $-\sqrt{0.64}$  

Multiple Select

Select the roots that have only a negative value. 

•  $\sqrt{121}$  

•  $-\sqrt{\frac{1}{36}}$  

•  $\pm\sqrt{\frac{289}{49}}$  

•  $-\sqrt{0.64}$  

Multiple Select

Select the roots that have both a positive and a negative value.

•  $\sqrt{121}$  

•  $-\sqrt{\frac{1}{36}}$  

•  $\pm\sqrt{\frac{289}{49}}$  

•  $-\sqrt{0.64}$  

Perfect Cubes & Cube Roots

• Index of 3

• Keep the sign under the radical

Multiple Select

How many of the expressions have a negative value?

•  $^3\sqrt{125}$  
  

•  $^3\sqrt{-1}$  
  

•  $^3\sqrt{-\frac{1}{64}}$  

•  $-^3\sqrt{-8}$  

The side length of a square.

• Two dimensional

• Use the area formula

   $A=s^2$  

• Remember that distance is always positive

The side length of a cube.

• Three dimensional

• Use the volume formula

   $V=s^3$  

• Remember that distance is always positive

Evaluating with Square Roots

• Follow the order of operations

• Radical Signs are Grouping Symbols ( )

Evaluating with Cube Roots

• Follow the order of operations

• Radical Signs are Grouping Symbols ( )

Solving equations with square roots

• Solution is both Positive & Negative

• Use the plus/minus sign

• List both solutions

Solving equations with cube roots

• Follow the sign

• Cubed root of a negative is negative

• Cubed root of a positive is positive

Multiple Select

Solve each equation. 

Select the equations with at least one solution of -2.

•  $x^2=4$  

•  $x^2=-4$  

•  $x^3=8$  

•  $x^3=-8$