Name:_______________________________________ Block:________ Date:___________ (SOL: 6.5)

45

Factors Numbers Words Exponential Form

4 4x4 Four to the second power

or four squared 42

2 222 Two to the third power or

Two CUBED 23

5 55 Five SQUARED

3 3333 Three to the fourth power

Square numbers, perfect squares and square roots

To find the square root of a number, find the number that when multiplied by itself is equal

to the number. *The root MAKES the larger number or the perfect square.

Example: √ = 4 because 4 x 4 = 16 or 42 is a square with 4 on each side On a square all sides are the same length and one side x the other = a perfect square.

-Word Bank for Exponents-

Exponent, Squared, Cubed, Exponential Form, Inverse Operations, Product Form/Standard Form, Base

43 42

3 x 3 x 3 x 3

Or

3 3 3

Multiplication is the opposite of Division

Addition is the opposite of Subtraction

Any number to the zero power is ALWAYS 1 (except 0)

34

Or

33

√ = 2 because…

2 is the length of each side.

Square Roots √ square root symbol

PERFECT SQUARES- Tell the square root for each perfect square.

36 = 6

Because 6 x 6 = 36 (The square root of 36 is 6.)

81 =

Because… 25 =

Because…

144 = Because…

49 =

Because…

36 =

Because…

400 =

Because…

121 = Because…

1 = Because…

Think about it… are the following perfect squares?

#’s Yes No Proof: Multiplication fact

25

5 x 5 = 25 All sides equal/square

12

48

49

0

2

100

56

1

What if it is NOT a perfect square?

The square root of a number that is not a perfect square falls between two consecutive

whole numbers.

Step 1: Is the number 29 a perfect square? Is there a whole number which can be squared

to equal 29?______________

Step 2: A) The number 25 is the closest perfect square less than 29. What is 25 ? -

_______________

B) The number 36 is closest perfect square greater than 29. What is 36 ? _______________

C) 29 lies between 25 and 36 . What are the two consecutive whole numbers

between which 29 lies? _______________________

Perfect Square #’s:

Square Roots: √

² =

2² =

3² =

4² =

5² =

² =

7² =

8² =

9² =

0² =

² =

2² =

3² =

4² =

5² =

² =

7² =

8² =

9² =

20² =

TRUE or FALSE? Show your work!

A) True or False 32 = 2

3

TRUE or FALSE? Show your work!

B) True or False 42= 2

4

Shade all PERFECT SQUARES

1) 25 = 2 x 2 x 2 x 2 x 2 Answer: 32

2) 34 3) 18

4) 91

5) 54 6) 72

7) 08

8) 43 9) 80

A) Write the following powers as a product of the same factor (product form, x x x )

1.) 45 = 2.) 36 = 3.) 83 =

B) Evaluate, or find the value of the given problems.

4.) 63 = 5.) 24 = 6.) 43 =

Finding the square root for NON-Perfect Squares.

* Find the two consecutive WHOLE NUMBERS between which the square root

of a given number lies/falls between.

1) 19 ________ __________ 2) 57 ________ __________

3) 48 ________ __________ 4) 99 ________ __________

5) 17 ________ __________

7) 22 ________ __________

9) 133 ________ __________

6) 2 ________ __________

8) 82 ________ __________

10) 320 ________ _________

C) Write the following numbers in exponential form (exponent form).

7.) Write 6 6 6 6 6 6 6 in exponential form.

8.) Write 8 8 8 8 8 8 8 8 8 8 8 in exponential form.

9.) Write 2 2 2 2 2 3 3 3 3 in exponential form.

What is the square root of each PERFECT square?

1) √ = 4 2) √25 =

3) √8 =

4) √ 00 =

5) √9 =

6) √3 =

7) √ 44 =

8) √ =

9) √49 =

10) √4 = 11) √ 4 = 12) √ 2 =

Write each expression in exponential form.

1) 4 x 4 x 4 x 4 x 4 x 4 _________________ 2) 8 x 8 x 8 x 8 x 8 x 8 x 8 x 8 _____________

3) 9 x 9 __________________ 4) p x p x p x p x p _______________

5) (10)(10)(10) _________________ 6) (14s)(14s)(14s) _______________

Find the square of each number. 4 squared = 4 x 4 = 42

1) 7 2) 13 3) 11 4) 1

5) 4 6) 10 7) 6 8) 8

Circle the numbers that are PERFECT squares:

6 18 36 49 55

64 73 100 122 169

Find the square root for each of the perfect squares

1) √ 44 = 2) √25 = 3) √8 =

4) √ 9 = 5) √ 25 = 6) √25 =

Estimate to find the two consecutive whole numbers between which the square root of a

given number lies.

1) √ 2 ______ ______ 2) √9 ______ ______ 3) √ 0 _____ ______

4) √3 ______ ______ 5) √ 70 _____ ______ 6) √55 ______ ______

7) √ 50 _____ ______ 8) √75 ______ ______ 9) √44 ______ ______

Compare the following values using <, >, or =.

1) 32 √ 4 2) 103 √4

3) √ 4 √8 4) 18 5

1