Unit #1 Review - Roots and Real Numbers

Cubes & Cube Roots

100

What is the difference between a square root and a cube root?

Square roots opposites with x²

Cube roots opposites with x³

200

The value of root(3)125 = x^3  What are the possible values of x.

x = 5

300

Find the cube root root(3)512

8

400

A cube has a volume of 1728 cubic inches. What is the length of one side of the cube?  x³ = 1728

12 in

500

If a number is Rational, does that is mean it is also an integer? Why or why not?

No because Integers cannot be decimals as they are only the positive and negative counting numbers on a number line. Rational numbers CAN have decimals or fractions. 

Squares & Square Roots

100

Evaluate the following expression

sqrt225

15

200

Find the square root of x = sqrt64 

x = +-8

300

Give the two square roots of the values:

x² = 441             x² = 81

x = +-21

x = +-9

400

Find the square root of sqrt-4

Can't solve. The negative needs to be outside the root. A squared numbers can't be negative.

500

Give the two square roots of the values:

x² = 169             x² = 729

x = +-13

x = +-27

Rational & Irrational

100

Determine if the following statement is true sqrt97 is Rational.

False

200

What is the difference between rational and irrational numbers?

Rational numbers can be written as both fractions and decimals that terminate or repeat

Irrational numbers cannot be written as fractions and are only decimals that are non-repeating & non-terminating

300

Classify the following numbers as either rational or irrational.

3.75     

-16    

sqrt135

Rational

3.75

-16

Irrational

sqrt135

400

Are the following rational or irrational numbers

6pi

root(3)18

-7.98

2pi/7

Rational

-7.98

Irrational

6pi

root(3)18

2pi/7

500

The statement is shown.

"The square root of x (sqrt x ) is a whole number."

Select all of the values of  sqrt x  that make the statement true.

A. x = 5     B. x = 9     C. x = 25     D. x = 98

B, C

Classifying Numbers

100

Define the following:

Integer

Whole Number

Natural Number

Integer - All positive & negative counting numbers

Whole Number - Positive counting numbers starting with 0

Natural Numbers - Positive counting numbers starting with 1

200

Why is the  sqrt57 considered an irrational number? 

It is a non-perfect square which means it results in a non-repeating & non-terminating decimal

300

Complete the following statements with sometimes, always, or never.

Integers will ________ be whole numbers.

Natural numbers will _____________ be whole numbers.

Irrational numbers will ________________ be rational.

Integers will sometimes be whole numbers.

Natural numbers will always be whole numbers.

Irrational numbers will never be rational.

400

Use Irrational, Rational, Integer, Whole Number, Natural Number

Classify the following real numbers:

-15

root(3)45

-15 -> Rational, Integer

3.55689... -> Irrational

500

Use Irrational, Rational, Integer, Whole Number, Natural Number

Classify the following real numbers:

sqrt144

-sqrt196

 

12 -> Rational, Integer, Whole, Natural

-14 -> Rational, Integer

Everything

100

List the following in order from greatest to least.

root(3)64

sqrt49

-sqrt64

root(3)27

sqrt49

root(3)64

root(3)27

-sqrt64

200

Two Equations are shown, where a>0. 

What is the value of b?

a^2 = 64

b = root(3)a

b = 2

300

Can there be a negative inside the square root?

ex. 

sqrt-x

No, 2 negatives always make a positive.

400

Travis Kelce wants to build Taylor Swift a beautiful rose garden building. He needs the building to be 343 cubic feet. What is the length of one side of the garden?

7 ft

500

What's happening tomorrow?

We have a Test!

(& 1st Pep rally)