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

Fill in the Blanks

The area of Mrs. Stein's square deck is 144 square feet. The side length is

ft.

Fill in the Blanks

The volume of a music box that is shaped like a cube is 512 cubic centimeters. The side length is

cm.

Evaluating with Square Roots

• Follow the order of operations

• Radical Signs are Grouping Symbols ( )

Fill in the Blanks

Evaluate the expression

 $2\sqrt{36}+9$  

Fill in the Blanks

Evaluate the expression

 $28-4\left(\sqrt{144}\right)^2$  

Evaluating with Cube Roots

• Follow the order of operations

• Radical Signs are Grouping Symbols ( )

Fill in the Blanks

Evaluate the expression

 $\left(^3\sqrt{-64}\right)^3+43$  

Fill in the Blanks

Evaluate the expression

 $18-^3\sqrt{27}$  

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.

•  $x^2=4$  

•  $x^2=-4$  

•  $x^3=8$  

•  $x^3=-8$