The Real Number System

Irrational/Rational

100

These rational numbers are referred to as "the counting numbers" and they include 1, 2, 3,...

Natural numbers

200

What is the difference between a rational number and an irrational number?

Rational numbers can be expressed as the quotient between two integers. Irrational numbers cannot. Irrational numbers are expressed as decimals that are infinite and not repeating. Irrational numbers cannot be expressed as fractions.

300

Is π  an irrational or a rational number?

Irrational

400

Is √2  a rational number or irrational?

Irrational

500

Is ∛343  a rational or irrational number?

Rational (∛343 = 7).

Intervals

100

What is a half open interval (a, b]? 

A set of numbers between a and b, including b but not including a. 

200

Draw (4, 8) on a number line. 

_________________________

       o___________o

      4                      8

300

Write  2 < x ≤ 3  in interval form then draw it. 

(2, 3]

________________________ 

   o______________@

   2                         3

400

Write  [–1, +∞)  as an inequality and draw it.

{x/ x ≥ -1 }

_______________________

        @------------------------>

        -1                            

500

For which values of x is the following expression true?

Square root of (x+2)(x-3)

 x ≤ –2 or if x ≥ 3

(-, -2] U [3, )

___________________________________

<-----------@                  @------------->

-          -2                  3                

Real Numbers

100

True or False: Some real numbers can be classified as both rational and irrational.

True

200

Is √169 natural, a negative integer, fractional, or irrational?

Natural (√169 = 13)

300

Is -√3 natural, a negative integer, fractional, or irrational?

Irrational.

400

Approximately represent  as a real number rounded to the hundredths place. 

3,85 (3,8464 rounded to the hundredths place)

500

What does  represent?

The golden ratio.

Roots

100

In the formula , what does a represent? 

The radicand. 

200

Express ∛64 as a power.

64^1/3

300

Simplify √18 in radical form.

√18 = 3√2

400

Simplify (√15)/(√20)=

(√3/4)

500

Rationalize the following: 

(√12)/(√7 + √3)

3√7−3√3 

see the answer here: https://www.mathway.com/popular-problems/Algebra/802735

Logarithms

100

What is log₂ 8 = ?

3

200

Write the equation log₃ 729 = 6 in exponential form.

3⁶ = 729

300

Solve log₄ 1,024 =

5

400

Solve log_{√ 2} 5 = (round to the nearest thousandth)

4.644

500

Solve log₂ 3 - log₂ 24 =

-3