Review of square roots, perfect squares, the real number system

Review of square roots, perfect squares, the real number system, and evaluating expressions

Some text here about the topic of discussion

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Squaring a number is raising that number to the power of ^two.

This tells you that you should multiply that number by itself. For example 5² means 5x5, which is just 25.

Taking the square root of a number is the opposite of squaring it. 

When simplifying square roots, knowing your perfect squares is very important.

Match

Match the following

• $$8\times6$$  

• $$9\times9$$  

• $$7\times8$$  

• $$12\times12$$  

• $$17\times17$$  

48

81

56

144

289

• 48

• 81

• 56

• 144

• 289

REVIEW: You will find the approximate square root of imperfect squares. 

REVIEW: Approximating Square Roots

REVIEW: Approximating Square Roots

Multiple Choice

Between which two whole numbers does the √32 fall?

• 4 and 5

• 5 and 6

• 6 and 7

• 7 and 8

Multiple Choice

In between what two integers is the  $$\sqrt{44}$$  ?

• 3 and 4

• 4 and 5

• 5 and 6

• 6 and 7

Multiple Choice

The $$\sqrt{56}$$  is in between which two whole numbers?

• 1 and 2

• 3 and 4

• 5 and 6

• 7 and 8

Multiple Choice

The $$\sqrt{37}$$  is in between which two whole numbers?

• 1 and 2

• 3 and 4

• 6 and 7

• 7 and 8

Multiple Choice

The $$\sqrt{78}$$  is in between which two whole numbers?

• 10 and 11

• 11 and 12

• 9 and 10

• 8 and 9

Learning Target

• I can classify numbers using The Real Number System.

Multiple Choice

Any of the numbers {0, 1, 2, 3} etc.

There is no fractional or decimal part. There are no negatives. These would be:

• Integers

• Whole Numbers

• Irrational Numbers

Multiple Choice

Numbers that can be used for counting. They do not include zero or negatives. What kind of numbers are they?

• Whole

• Counting

• Integers

Number System

Multiple Choice

Is the number. 0.64646464... rational or irrational?

• Irrational because it is nonterminating.

• Rational because it is repeating.

• Irrational because it is an imperfect square.

• Rational because it terminates.

Multiple Choice

The number 9, classifies as all of the following groups except which one?

• Natural

• Whole

• Irrational

• Real

Multiple Choice

Is 36 a natural number?

• Yes

• No

Multiple Choice

Is the fraction 4/5 a natural number?

• Yes

• No

Multiple Choice

Which of the following is NOT a whole number?

• 0

• 3

• 0.4

• 12

Multiple Choice

Which of the following is an integer?

• $$\frac{1}{2}$$  

• 0.53

• -9

• -1.6

Match

Match the following to the BEST (most exact) category that it belongs to

• 0

• 5

• -4

• $$0.\overline{3}$$  

• $$\pi$$  

whole number

natural number

integer

rational

irrational

• whole number

• natural number

• integer

• rational

• irrational

Evaluating an expression means plug a number in for the variable.

• This is also called "substitution"

• Example: Evaluate 2x + 5 when x = 4

Multiple Select

In the order of operations, which one comes first?

• Exponents

• Addition

• Multiplication

Multiple Choice

$$What\ is\ the\ first\ step?\ \ \ 3^2-\left(1+2\right)+5\times2\div2$$  

• First Do  $$3^2$$  

• Do (1+2) first

• Do multiply first

• divide first

GEMDAS

• G - grouping

• E - exponents

• M - multiplication

• D - Division

• A - Addition

• S -

Multiple Choice

The grouping in GEMDAS stands for?

• Commas, Periods, Question Marks

• Exponents, Multiplication, Division

• Brackets, Braces, Parentheses

• Subtraction, Addition, Multiplication

Multiple Choice

What operation would you do first in this expression?

• 15-8

• $$8\div4$$

• 4 x 7

Multiple Choice

Which operation would you perform first between addition and subtraction?

• You do subtraction first.

• With subtraction and addition, you go left to right.

• You do addition first.

Multiple Choice

Solve: $$\left(10-5\right)^2+\left(12\div4\right)$$  

• 13

• 28

• -22

• 7

Multiple Choice

Solve: $$5-2\left(2^3-5\right)$$  

• -1

• 3

• -9

• 9

Replace variables with the numbers given.

If x = 5, replace the x with a 5.​

​

​Evaluating Expressions and Order of Operations

​Evaluating Expressions

​

Fill in the Blanks

Multiple Choice

Evaluate the expression:

$$6^2-4\div2$$  

• 4

• 34

• 16

• 10

Watch the video on the next slide to remember how to use DESMOS to evaluate expressions.

Multiple Choice

Evaluate the expression. $$\left(8-5\right)\cdot12+3^2$$  

• 54

• 42

• 63

• 45

Multiple Choice

Which student correctly used the order of operations while solving this problem?

Multiple Choice

Evaluate the expression when x = 2 and y = 4. $$\frac{16\ +\ 2x}{y\ +\ 1}$$   

• 18

• 4

• 20

• 5

Multiple Choice

Evaluate -2x  if     x = 10

• -8

• 20

• -20

Multiple Choice

b² + 4
when b = 3

• 10

• 12

• 13

• 11