Squares and Square Roots

Review of square roots, perfect squares, the real number system, and compare and order numbers

Some text here about the topic of discussion

Let's try it!

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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

Ordering Rational Numbers

Objective: Order rational numbers on a number line.

Multiple Choice

Make the percent to decimal.

142%

• 1.42

• 14.2

• 0.142

Multiple Choice

Make the percent to decimal.

7%

• .007

• 0.07

• 7

Multiple Choice

Place numbers from least to greatest.

• -3/7, -0.44, √2, 0.14, 141%,

• -0.44, 0.14, -3/7, √2, 141%

• -3/7, -0.44, 0.14, 141%, √2

• -0.44, -3/7, 0.14, 141%, √2

Multiple Choice

Point B could represent which of the following numbers?

• √24
• √30
• √35
• √42

Multiple Choice

Put in the symbol to make the statement true...
-17.5   _________ -√121

• >
• <
• =

Multiple Choice

Which list of numbers is in order from least to greatest?

• A √23, 5, 6, 43%
• B 5, √23, 6, 43%
• C 43%, 5, √23, 6
• D 43%, √23, 5, 6

Multiple Choice

List the following numbers from least to greatest:
-64 , 3.5 , √27 , 6.666...

• -64 , 3.5 , √27 , 6.666...
• 3.5 , √27 , 6.666..., -64
• 3.5, -64, √27, 6.666...
• 6.666, √27, -64, 3.5